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11

Socializing by Gaming: Revealing Social Relationships in Multiplayer

Online Games

ADELE LU JIA*,SIQISHEN,RUUDVANDEBOVENKAMP,ALEXANDRUIOSUP,

FERNANDO KUIPERS, and DICK H. J. EPEMA,DelftUniversityofTechnology

Multiplayer Online Games (MOGs) like Defense of the Ancients and StarCraft II have attracted hundreds of

millions of users who communicate, interact, and socialize with each other through gaming. In MOGs, rich

social relationships emerge and can be used to improve gaming services such as match recommendation and

game population retention, which are important for the user experience and the commercial value of the

companies who run these MOGs. In this work, we focus on understanding social relationships in MOGs. We

propose a graph model that is able to capture social relationships of a variety of types and strengths. We apply

our model to real-world data collected from three MOGs that contain in total over ten years of behavioral

history for millions of players and matches. We compare social relationships in MOGs across different game

genres and with regular online social networks like Facebook. Taking match recommendation as an example

application of our model, we propose SAMRA, a Socially Aware Match Recommendation Algorithm that takes

social relationships into account. We show that our model not only improves the precision of traditional link

prediction approaches, but also potentially helps players enjoy games to a higher extent.

Categories and Subject Descriptors: C.2.2 [Computer-Communication Networks]: Network Protocols

General Terms: Design, Algorithms, Performance

Additional Key Words and Phrases: Multiplayer Online Games (MOGs), social relationship, user interaction,

graph model

ACM Reference Format:

Adele Lu Jia, Siqi Shen, Ruud van de Bovenkamp, Alexandru Iosup, FernandoKuipers, and Dick H. J. Epema.

2015. Socializing by gaming: Revealing social relationships in multiplayer online games. ACM Trans. Knowl.

Discov. Data 10, 2, Article 11 (October 2015), 29 pages.

DOI: http://dx.doi.org/10.1145/2736698

1. INTRODUCTION

Multiplayer Online Games (MOGs) are games in which multiple players can play in

the same online game environment at the same time. They have attracted hundreds of

millions of people worldwide who communicate, interact, and socialize with each other

through gaming. They represent a large economic sector that covers an entire ecosystem

∗Jia is currently working in the Information and Electrical Engineering Department at the China Agricul-

tural University.

This work is partially supported by the National Basic Research Program of China under grant No.

2011CB302603, and the Dutch STW/NWO Veni personal grant @ large (#11881).

Authors’ addresses: A. L. Jia, S. Shen, A. Iosup, and D. H. J. Epema, Department of Software and

Computer Technology, Delft University of Technology; emails: adele.lu.jia@gmail.com; {S.Shen, A.Iosup,

D.H.J.Epema}@tudelft.nl; R. van de Bovenkamp and F. Kuipers, Department of Intelligent Systems, Delft

University of Technology; emails: {R.vandeBovenkamp, F.A.Kuipers}@tudelft.nl.

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DOI: http://dx.doi.org/10.1145/2736698

ACM Transactions on Knowledge Discovery from Data, Vol. 10, No. 2, Article 11, Publication date: October 2015.

11:2 A. L. Jia et al.

of entertainment products, and that is worth billions of US dollars worldwide. Some

MOGs, for example, Defense of the Ancients (DotA) and StarCraft II, have featured

in several tournaments with wide appeal to gamers and game watchers, such as, the

World Cyber Games (WCG) and the Electronic Spo rts Wo rld C up (E SWC). From the

vast user base of MOGs, rich social relationships emerge that are useful for improving

gaming services such as match recommendation and game population retention. Thus,

it is important to understand the social relationships in MOGs, and this constitutes

the purpose of this paper.

Different from single-player games that put players against program-controlled op-

ponents, MOGs allow players to enjoy interactions with other human beings—they may

compete with each other individually, they may work cooperatively as a team to achieve

acommongoal,theymaysuperviseactivitiesofotherplayers,ortheymayengageina

game genre that incorporates any possible combination of these types of interactions.

Often, these interactions provide players with a form of social communication, from

which various types of social relationships may emerge that can be used for improving

gaming services. For example, plain adversarial relationships in MOGs can be used to

promote user activity—players who want to beat each other may motivate each other

to stay longer as game customers.

An increasing number of social network analyses [Newman 2003] use graphs to rep-

resent user relationship, including explicit relationships like friendship [Garg et al.

2009; Kairam et al. 2012; Hu and Wang 2009], and implicit relationships like user

interactions [Wilson et al. 2009; Viswanath et al. 2009; Leskovec et al. 2005; Xiang

et al. 2010; Liu et al. 2012]. Often, graphs are extracted from one or multiple snap-

shots of the network based on a single,domain-speciﬁc, and usually threshold-based

rule for mapping relationships to links. Taking Facebook as an example, the map-

ping rule can be that any two users who have exchanged messages for more than

ten times are mapped to two nodes connected by one link in the graph. For three

reasons, this traditional approach is insufﬁcient to obtain clear social relationships

and their evolution from an MOG. First, network snapshots can be generated in

various ways, for example, with or without considering the history before the last

snapshot. However, the inﬂuence of different snapshot generation methods on the in-

ferred relationship evolution has only been partially investigated before Viswanath

et al. [2009], Leskovec et al. [2005], Ribeiro et al. [2013], Caceres and Berger-Wolf

[2013], and Krings et al. [2012], and a detailed comparison between these methods is

needed. Secondly, gaming involves relationships in various domains that normally do

not exist in regular social networks, for example, winning together and competing with

each other. To infer user relationships in MOGs, these domains need to be carefully

examined and compared. Thirdly, the impact of various graph extraction rules and

thresholds employed has received relatively little attention [Choudhury et al. 2010],

and a thorough analysis on how they inﬂuence the structure of the resulting graphs is

needed.

To tackle the af orementioned is sues, in this paper, we propose a graph model that

is able to capture social relationships of a variety of types and strengths. We apply

our model to real-world datasets to analyze social relationships and their evolution in

MOGs. As it turns out, our model is able to identify important relationships in MOGs,

including “wingmen” that are very likely to play together in the future and adversary

relationships that are useful for population retention. By investigating network evo-

lution from different perspectives, our model also demonstrates how an MOG can still

exhibit growth while its player activity actually declines. Taking match recommenda-

tion as the example, we demonstrate how to apply the social relationships revealed

by our model to improve gaming services. Our results show that our model not only

improves the precision of traditional link prediction approaches, but also potentially

ACM Transactions on Knowledge Discovery from Data, Vol. 10, No. 2, Article 11, Publication date: October 2015.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:3

helps players enjoy games to a higher extent. We summarize our main contributions

as follows.

(1) We collect, use, and offer public access to datasets representative for three popular

MOG genres. The datasets contain in total ten years of behavioral history for

1,120,049 players and 2,248,045 matches (Section 3). The datasets are publicly

available through the Game Trace Archive (http://gta.st.ewi.tudelft.nl/).

(2) We propose a graph model to analyze social relationships in MOGs, based on

which we study the inﬂuence of relationship strength on the extracted graphs

(Section 4), we analyze the mutual inﬂuence of friendship and interactions

(Section 5), and we demonstrate user behavioral changes and the resulting net-

work evolution in MOGs (Section 6).

(3) Based on the social relationships revealed by our model, we propose SAMRA, a So-

cially Aware Match Recommendation Algorithm that we compare with traditional

link prediction approaches (Section 7).

2. PROBLEM STATEMENT

In this section, we ﬁrst introduce MOGs, matchmaking, and social relationships in

MOGs. Then, we state the research questions we study in this paper.

2.1. An Overview of MOGs

MOGs are games in which multiple players can play in the same online game environ-

ment at the same time. Players in MOGs often control in-game avatars and, individ-

ually or team wise, they try to conquer the opposite side’s territory. Within MOGs, a

variety of game genres exist. Throughout this paper, we consider three popular game

genres, namely Real-Time Strategy (RTS) games exempliﬁed by StarCraft II, Multi-

player Online Battle Arenas (MOBAs) exempliﬁed by DotA, and Massively Multiplayer

Online First-Person Shooter (MMOFPS) games exempliﬁed by World of Tanks.

Different game genres often have different match scales that specify a limit on the

number of players per team, and in-game targets that reﬂect the design emphasis of

the game genres. Regarding the match scale, DotA requires exactly ﬁve players per

team (we indicate this by “5v5-player”), whereas StarCraft II and World of Tanks allow

players to form teams of different sizes, with a maximum of 8 and 15 players per team,

respectively. Regarding in-game targets, StarCraft II asks players to balance strategic

and tactical decisions, often every second, while competing for resources with other

players. DotA provides the opportunity for teams of players to confront each other on a

map and try to conquer the opposite side’s main building. And World of Tanks, although

fast paced, tests the tactical team work of players disputing a territory. Intuitively, from

StarCraft II to DotA and further to World of Tanks, the requirement of team cooperation

increases. As a consequence, we observe an increasing trend in their match scale—92%

of the matches in our StarCraft II dataset are 1v1-player, all matches in DotA are ex-

actly 5v5-player, and 98% of the matches in our World of Tank dataset are 15v15-player.

Seeing MOGs in a broader perspective, they are online social networks in which

users socialize with each other through gaming. Here, we classify online social net-

work into two categories, viz., socializing-driven and target-driven networks. Different

from typical socializing-driven networks like Facebook, in which users mainly join to

socialize with their online and ofﬂine friends, MOGs are target driven and their users

primarily join and interact for a particular target, that is, games. Other typical target-

driven networks include YouTube, Flickr, and Meetup, in which users interact through

cocommenting on the same video, coviewing the same photo, and coparticipating in

the same event. As in many other online social networks, users in MOGs may develop

various social relationships.

ACM Transactions on Knowledge Discovery from Data, Vol. 10, No. 2, Article 11, Publication date: October 2015.

11:4 A. L. Jia et al.

It should be noted that our classiﬁcation here is loose: it often happens that users in

target-driven networks also seek to socialize with others. Nevertheless, we still use this

classiﬁcation to distinguish the premier purposes of different online social networks.

As a matter of fact, we observe interesting patterns based on this classiﬁcation (as we

will show later in Section 5.2).

2.2. Matchmaking in MOGs

As we focus in this paper on understanding the social relationships emerging from

MOGs, it is important to know how matchmaking works, that is, how users are

paired/grouped into the same game. Normally, different matchmaking methods are em-

ployed by MOG communities. In this paper, we consider four MOG communities, that

is, two DotA communities, Dota-League and DotAlicious, one StarCraft II community,

and one World of Tanks community (details of these communities will be introduced

later in Section 3.1). We introduce their matchmaking methods in turn as follows.

In Dota-League, players who want to play a match ﬁrst join a waiting queue. When

there are ten or more players in the waiting queue, the matchmaking algorithm will

form teams (each with ﬁve players) that are balanced in terms of the skill levels of the

players. Although this matchmaking algorithm enforces balanced matches, it does not

take into account the social relationships of the players. As a consequence, we observe

that 41% of the games in Dota-League are aborted at the very beginning of the match.

Because quitting at the start of the game could be the outcome of players expressing

their disagreement with the matchmaking system’s choice, we omit these 41% games

in our later analysis and assume that the formations in the remaining games are

according to players’ satisfaction.

In DotAlicious, each game server has a number of open matches waiting for players

to join, and each arriving player can select which match to join and on which team.

For StarCraft II, users ca n choos e either to organiz e games by themselv es (the so-

called custom game), or to be assigned by the community to games with other players

with similar skill levels (the so-called ladder game). World of Tanks uses a similar

matchmaking method as StarCraft II.

To sum up, under the aforementioned matchmaking methods, users can choose their

teammates and opponents freely, either by organizing the games directly, or by quit-

ting playing with unintended players. Therefore, the gaming experiences in the four

MOG communities we consider are suitable proxies for inferring spontaneous social

relationships.

2.3. Social Relationships in MOGs

Social relationships in MOGs can be explicit or implicit.Explicitrelationshipsare

formed on players’ own initiative, for example, when players personally establish

friendships with others, or join a clan (a self-organized group of players who often

form a league and play on the same side in a match). Implicit relationships, on the

other hand, are formed passively by players, for example, through interactions.

Explicit relationships are precise, but they are not sufﬁcient to capture various

social relationships in MOGs. One reason is the prosocial emotions involved through

gaming, for example, vicarious pride and happy social embarrassment [McGonigal

2011]. Another reason is the rareness of explicit relationships like friendship. When

explicit relationships are not enough, implicit relationships, such as user interactions,

provide the supplementary information for inferring social relationships. For example,

we observe that in Dota-League, less than 10% players have explicitly identiﬁed more

than ten friends, while 50% players have played repeatedly and possibly regularly with

more than 50 players.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:5

In MOGs, users interact with each other in various ways, for example, by joining

the same match, by playing on the same/opposite sides, and by winning/losing to-

gether. These interactions are straightforward and yet important: joining the same

match is a precondition for interaction, playing on the same/opposite side indicates a

positive/adversarial relationship, and winning/losing together may impact player at-

titude and their future team formation. These interactions will help us to infer social

relationships in MOGs.

2.4. Research Questions

In this paper, we answer the following ﬁve research questions.

(i) How can we infer social relationships from MOGs?

User relationships provide important information for improving services in online

social networks. However, most previous work is based on explicit relationships like

friendship [Garg et al. 2009; Kairam et al. 2012; Hu and Wang 2009] or simply treats

various types of interactions equally [Wilson et al. 2009]. In contrast, we propose a

graph model that takes a variety of types of interactions into account.

(ii) How are MOGs different across game genres and from regular online social net-

works at the structural level?

This question helps us to understand the differences between social networks. In

this paper, we apply our model to real-world data collected from three MOGs. We then

compare our results with previous studies on regular online networks [Wilson et al.

2009; Viswanath et al. 2009; Mislove et al. 2007; Liu et al. 2012], including Facebook,

YouTu b e , L i n kedI n , a n d M eet u p .

(iii) How are networks representing explicit and implicit relationships in MOGs

related?

The correlation between explicit and implicit relationships is useful for relationship

prediction. For example, we can predict potential interactions of a user based on his

current friendships with others. We answer the aforementioned question by comparing

properties of the graphs representing friendship and interactions.

(iv) How do MOGs evolve over time?

Network evolution reﬂects general user activity change, and provides important in-

formation for system operation. Previous evolution models are mostly based on friend-

ship [Garg et al. 2009; Kairam et al. 2012; Hu and Wang 2009]. A few models [Viswanath

et al. 2009; Leskovec et al. 2005] include user interactions, but they only consider one

perspective on network evolution. In contrast, we investigate network evolution from

different perspectives by demonstrating how an MOG can still exhibit growth while its

player activity actually declines.

(v) What are possible applications of our model?

We take match recomm end ati on as t he ex ample to study the application of our model

to gaming services. Good match recommendation algorithms improve user experience

and hence the commercial value of MOGs, but they are often neglected or designed in

acasualway.Totacklethisissue,weproposeasociallyawarealgorithmbasedonour

model, and we show that our model improves the quality of match recommendation.

3. A MODEL FOR MOGS

In this section, we ﬁrst introduce the datasets we collected from three MOGs. Then,

we propose a graph model for analyzing social relationships in MOGs.

3.1. Datasets of MOGs

Players in MOGs are often loosely grouped into large communities. Each of these com-

munities operates its own game servers and provides various gaming services, such as

matching players to games, maintaining lists of match results and user proﬁles, and

11:6 A. L. Jia et al.

Table I. Dataset Statistics of Four MOG Communities

Community Game Genre Team Size No. of Players No. of Matches Obtained History

Dota-League MOBAs Exactly 5v5 61,198 1,470,786 2008.11–2011.7

DotAlicious MOBAs Exactly 5v5 62,495 617,069 2010.4 –2012.2

StarCraft II RTS Mostly 1v1 83,199 85,532 2012.3–2013.8

World of Tan ks MMOFPS Mostly 15v15 913,157 74,658 2010.8–2013.7

Game Genre and Team Size are as Introduced Earlier in Section 2.

publishing player ranking information. We have collected datasets from four MOG com-

munities, that is, two DotA communities, Dota-League and DotAlicious, one StarCraft

II community, and one World of Tank community.

In these communities, each user possesses a user proﬁle page, which shows his friend

list and clan membership. Each match has a match page that shows the start and end

times of the match, the player list, and the result of the match (winning team, draw, or

abort). We have crawled each of these user proﬁles and match pages at least twice, to

reduce the effect of possible temporary unavailability and trafﬁc shaping of the website.

To sanitize the data, we have ﬁltered out matches with zero duration. In the end, we

have obtained the full history of the four MOG communities and in total four types of

datasets: (i) the friendship dataset from Dota-League, (ii) the clan membership dataset

from DotAlicious, (iii) the user skill level datasets from Dota-League and DotAlicious,

and (iv) the match datasets for all four communities. Statistics of these datasets can

be found in Table I.

In general, the two DotA communities, Dota-League and DotAlicious, achieve popula-

tions of similar sizes. Because Dota-League has been operated longer than DotAlicious,

it has more matches. World of Tanks achieves the largest population but the fewest

matches. We believe this is because it has the largest match scale: most matches in

World of Tanks are 15v15-play er, whereas matches in DotA an d Sta rCr aft I I are 5v5-

player and (mostly) 1v1-player. A more detailed description of the datasets can be found

in our previous work [van de Bovenkamp et al. 2013; Iosup et al. 2014].

3.2. Graph Models for MOGs

Following social netwo rk analysis, we use graph-ba sed models to represent user rela-

tionships in MOGs. We propose the following two types of graphs, in both of which the

nodes represent the players:

3.2.1. Friendship Graph.

In the friendship graph,alinkbetweentwonodesrepresents

the friendship between the corresponding players. Friendship graphs are undirected

and unweighted.

3.2.2. Interaction Graph.

Following previous work on Faceb ook [Wilson et al. 2009 ], in

an interaction graph,alinkbetweentwonodesrepresentsinteractions,intermsof

games, between the corresponding two players. Unlike in Wilson et al. [2009], in which

all interactions are assumed to be homogeneous, we consider ﬁve types of interactions

and we extract ﬁve interaction graphs as follows:

(1) SM: two players present in the Same Match;

(2) SS: two players present on the Same Side of a match;

(3) OS: two players present on the Opposite Sides of a match;

(4) MW: two players who Won together in a match;

(5) ML: two players who Lost together in a match.

Interaction graphs are undirected and unweighted; we do not use link weight to

capture the interaction strength. Instead, we map interactions to links by applying a

threshold-based rule, and only interactions with enough strength to pass the thresholds

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:7

will be included in the graph. We consider two mapping thresholds:theperiodtof effect

for a user interaction, and the minimum number nof interactions that need to have

occurred between two users for a relationship to exist. For example, in an SM graph

with tequal to one week, and nequal to 10, a link between two players exists only if

there is at least one week in which they have played at least ten games together.

It is obvious that both a small value of tand a large value of nimpose strong

relationship constraints. Meanwhile, for the same values of tand n, there are fewer

relationship constraints in the SM graph than in the SS and OS graphs, which in turn

have fewer relationship constraints than the ML and MW graphs. Thus, by tuning t

and nfor our ﬁve interaction graphs, our model can capture relationships with various

strengths. We explore this in more detail in Section 4.

The list of the ﬁve interaction graphs we propose here is not exhaustive and it

can support more complex variations. For example, it can incorporate more speciﬁc

interactions, such as playing against each other at least ten times, in the winter, while

located in the same country. It can also support more mapping thresholds. For example,

opposite to n, we can specify a maximum number of interactions between two users for

a relationship to exist. In this way, we can focus on moderately interacting user pairs,

which often consist the majority of an MOG’s population.

3.3. Graph Metrics

To study the social relationships in MOGs, we com pare their friend ship and interaction

graphs based on a number of graph metrics that are related to the degrees and paths

between players. Speciﬁcally, we consider the following graph metrics.

Network size (N): The number of nonisolated nodes in a graph; NLCC represents the

size of the Largest Connected Components (LCC) and NLCC/Nrepresents the fraction

of nodes in the LCC.

Number of links (L): The number of links in a graph; LLCC represents the number of

links in the LCC.

Degree (d): The degree of a node is the number of its neighbors.

The distance (h): The distance between two nodes is equal to the length of a shortest

path between them.

Diameter (D): The diameter is the largest distance between any two nodes.

The clustering coefﬁcient (C ): The clustering coefﬁcient (CC) of a node is equal to the

fraction of pairs of its neighbors that are linked.

Assortativity (ρ): Assortativity is the average Pearson Ranking Correlation Coefﬁ-

cient (PRCC) of degree between pairs of connected nodes. In brief, PRCC measures the

linear dependence between two variables. Therefore, assortativity measures to what

extent nodes link to other nodes with similar degrees.

4. USER RELATIONSHIP AND NETWORK STRUCTURE

The graph model proposed in Section 3 identiﬁes relationship types and strength in

MOGs by differentiating gaming relationships (SM, SS, OS, MW, and ML) and by

using mapping thresholds (nand t). In this section, we analyze the inﬂuence of the

gaming relationship and the values of the thresholds on the structural properties of

the graphs generated by our model. In general, the patterns we observe for the four

MOG communities we consider are rather similar, and therefore, here we only show

the results for Dota-League.

4.1. Inﬂuence of Interaction Strength: Threshold

n

Here, we set the period of effect tto ∞and we vary the minimum number of interactions

nfrom 4 to 500. We choose this range for nbecause, as we will show later, it captures

the important changes of the graph structure: when nincreases from 4 to 500, the

11:8 A. L. Jia et al.

Fig. 1. The inﬂuence of the minimum number of interactions that need to have occurred between two users

for a relationship to exist (threshold n) on the network structure (the vertical axis has a logarithmic scale).

graph starts to dissolve from a giant connected component to a number of relatively

small connected components. For every value of n,wegenerateasetofﬁveinteraction

graphs from the dataset of Dota-League, one for each gaming relationship. We show

the properties of these interaction graphs in Figure 1.

Network Size: As shown in Figure 1(a) and 1(b), for any of the interaction graphs,

its network size and the fraction of nodes in the LCC drop quickly (near exponentially)

as the threshold nincreases, and after nincreases to a very large value1, the fraction

of nodes in the LCC starts to increase with n. Apparently due to the dramatically

decreased network size, it becomes easier for the remaining nodes to be connected.

Intuitively, for pairs of players who play intensively with each other, the increase

of nshould not inﬂuence their links very much, since they have played far more than

ngames. We conjecture that less-intensively playing players form the less strongly

connected fringe in the LCC, and that as nincreases, their links are removed ﬁrst

and they are removed from the LCC—in other words, the core of the graph will be

more strongly connected as nincreases. This conjecture is conﬁrmed by the following

observation on the network connectivity.

Network Connectivity: As shown in Figure 1(c), for any of the interaction graphs, the

average clustering coefﬁcient increases with nuntil n∼20, stays stable after that, and

starts ﬂuctuating from n∼50. This result conﬁrms our conjecture that as nincreases,

the less strongly connected fringe is removed and the LCC is getting more strongly

connected. On the other hand, when nbecomes very large, links from the core of the

graph are also removed. The combination of these two forces makes the clustering

coefﬁcient unstable for large values of n.

1This turning point is different for different interaction graphs.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:9

Fig. 2. The inﬂuence of the period of effect, that is, the threshold t(network size normalized to the case of

t=∞).

Default Value of n for Later Analysis: To avoid repeatedly exploring the mapping

thresholds, here we choose the default value of nfor our later analysis. On the one

hand, ncannot be too large, otherwise it induces a very strong relationship constraint

and the network will be overly fragmented. On the other hand, ncannot be too small

either, otherwise it achieves a small clustering coefﬁcient and it will be difﬁcult to dif-

ferentiate strong user relationships from occasional or even random ones. Given these

considerations, we choose n=10 for Dota-League, in which for any of the interaction

graphs at least half of the nodes are in the LCC and the average clustering coefﬁcient is

almost at its maximum, which guarantees a strongly connected LCC with a reasonable

size. Following the same rules, we choose n=10, 2, and 4 as the default values for

DotAlicious, StarCraft II, and World of Tanks, respectively.

4.2. Inﬂuence of Interaction Type

As shown in Figure 1, for the same value of n, the network size and the fraction of nodes

in the LCC in the SM graph are larger than those in the OS and SS graphs, which in

turn are larger than those in the MW and ML graphs. When nincreases, these metrics

drop faster in the MW and ML graphs than in the OS and SS graphs, which in turn drop

faster than in the SM graph. One simple explanation is that there are fewer links in

graphs extracted using stronger relationship constraints (e.g., MW and ML, or OS and

SS compared to SM), and thus removing links from them breaks down the graph more

quickly than graphs that are extracted using less restrictive relationship constraints.

4.3. Inﬂuence of the Period of Effect: Threshold

t

Given the similarity in the network structure of the ﬁve interaction graphs we model,

here we focus only on the SM graph. We set n=10 and vary tfrom one day, to one week,

one month, and inﬁnity. The results are shown in Figure 2. With an increasing value of

t,therelationshipconstraintsgetlessstrict,andsothenetworksizeandthefractionof

nodes in the LCC are increased, although compared to Figure 1, they are not increased

as quickly as when we decrease n. Meanwhile, the average clustering coefﬁcient does

not change much with t. These results indicate that nhas a higher inﬂuence on the net-

work structure than t, and we compare the inﬂuence of nand tin the following section.

4.4. Comparison of the Inﬂuence of

n

and

t

As shown in Figure 3(a) and 3(b), for a ﬁxed value of n,decreasingtcan at most reduce

the network size by 20,000 and the fraction of nodes in the LCC by 50% (when n=20),

whereas for a ﬁxed value of t, decreasing ncan easily reduce the network size by over

30,000 and the fraction of nodes in the LCC by over 80%.

Together with the results from the previous sections, we conclude that when the

constraints for a relationship to exist get stricter, the graphs representing those

relationships become more disconnected, but the connection between nodes in their

11:10 A. L. Jia et al.

Fig. 3. The inﬂuence of the minimum number of interactions that need to have occurred between two users

for a relationship to exist (threshold n) and the period of effect (thresholds t) on the network structure (the

vertical axis in (b) and (c) has a logarithmic scale).

LCCs becomes stronger. Further, increasing nand decreasing t—two methods to ex-

tract more strict relationships—have similar inﬂuence on network structure, with

increasing nhaving a stronger effect.

5. FRIENDSHIP AND INTERACTION GRAPHS

In this section, we analyze the similarities, the differences, and the correlation between

the friendship and interaction graphs of the four MOG communities we consider. To

generate the interaction graphs, we use the default values for the mapping thresholds

we chose in Section 4, that is, the period of effects for interactions tis set to ∞,andthe

minimum number of interactions nis set to 10, 2, and 4 for Dota-League and DotAli-

cious, StarCraft II, and World of Tanks, respectively. To compare different MOGs at the

same activity level, we also test n=10 for StarCraft II and World of Tanks. An overview

of the values of the graph properties is presented in Table II. In general, we ﬁnd that

both the friendship and interaction graphs of the four MOG communities we consider

exhibit the small-world property, that friendship has a positive inﬂuence on user inter-

actions, and that MOGs of game genres have different user interaction patterns.

5.1. The Small-World Property

As shown in Table II, both the friendship and interaction graphs have relatively small

average hop counts and rather high average clustering coefﬁcients, indicating that they

possess small-world properties [Milgram 1967], [Watts and Strogatz1 1998] rather than

the properties expected of random graphs.2

5.2. Degree Distribution

Instead of ﬁnding accurate degree distributions, we are more interested in under-

standing the difference in the degree distributions of the graphs representing different

relationships. We use a power-law distribution as the comparison baseline, since node

degrees in many social networks are found to follow this distribution [Mislove et al.

2007; Wilson et al. 2009; Liu et al. 2012]. We use the Maximum Likelihood Estimation

method [Clauset et al. 2009] to perform power-law curve ﬁtting for node degrees in the

friendship and interaction graphs, and we compare whether one is heavier, similar, or

lighter-tailed than another.

Figure 4 shows the results of Dota-League. The straight dashed lines in these ﬁgures

are the ﬁtted power-law distributions. We see that the degree distribution of Dota-

League’s friendship graph is power-law distributed, and those of its interaction graphs

2Random graphs have clustering coefﬁcient equal to K/N, where Krepresents the average node degree and

Nrepresents the number of nodes.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:11

Table II. Properties of Friendship and Interaction Graphs Extracted From Four MOG Communities

DotA-League (n=10) DotAlicious (n=10)

SM OS SS ML MW FR SM OS SS ML MW

N31,834 26,373 24,119 18,047 18,301 53,062 31,702 11,198 29,377 22,813 21,783

NLCC 27,720 19,814 16,256 6,976 8,078 34,217 26,810 10,262 20,971 10,795 13,382

L202,576 85,581 62,292 30,680 33,289 368,854 327,464 92,010 108,176 43,240 54,009

LLCC 199,316 79,523 54,186 17,686 21,569 301,586 323,064 91,354 99,063 29,072 44,129

¯

h4.42 5.40 6.30 8.09 7.67 8.1 4.24 3.97 5.3 6.80 5.95

D14 21 24 28 26 26 17 12 19 20 22

¯

C0.37 0.40 0.41 0.41 0.41 0.3 0.43 0.27 0.47 0.47 0.49

ρ0.13 0.26 0.25 0.27 0.28 0.22 0.08 0.01 0.25 0.27 0.29

StarCraft (n=10) World of Tan ks ( n=10)

SM OS SS ML MW SM OS SS ML MW

N907 611 314 95 212 4,340 477 4,251 561 1,824

NLCC 31 22 24 9 14 129 118 122 66 57

L748 404 327 85 200 9,895 3,253 6,543 1,564 2,923

LLCC 58 21 44 13 24 2,329 1,243 1,160 519 473

¯

h1.88 4.04 1.90 1.64 1.74 1.88 2.00 2.18 2.080 1.78

D28322 63 5 43

¯

C0.58 0 0.70 0.65 0.65 0.79 0.10 0.78 0.88 0.87

ρ−0.46 −0.45 −0.42 −0.58 −0.53 −0.10 −0.12 −0.06 −0.03 −0.10

StarCraft (n=2) World of Tan ks ( n=4)

SM OS SS ML MW SM OS SS ML MW

N83,199 83,199 25,556 13,995 10,736 78,226 15,618 68,659 27,605 28,274

NLCC 68,335 68,335 6,221 565 2176 20,555 4,932 8,444 163 2,911

L156,941 125,371 32,489 15,671 13,513 212,103 81,225 124,600 52,697 58,532

LLCC 143,892 113,994 11,907 1,139 3,983 145,141 35,615 38,671 799 14,877

¯

h7.21 7.58 7.23 3.94 6.62 9.85 13.55 12.42 3.30 17.98

D29 29 19 12 18 31 35 39 9 47

¯

C0.31 0.05 0.79 0.89 0.82 0.56 0.01 0.61 0.71 0.71

ρ−0.07 −0.09 −0.12 −0.16 −0.17 0.06 0.09 0.17 −0.003 −0.14

The Metrics we Present are the Number of Nodes N, the Number of Nodes in the LCC NLCC, the Number

of Links L, the Number of Links in the LCC LLCC, the Average Hop Count ¯

h, the Diameter D,theAverage

Clustering Coefﬁcient ¯

C,andtheAssortativityρ.

Fig. 4. The degree distributions of the friendship and interaction graphs of Dota-League. Straight dashed

lines show the ﬁtted power-law distributions.

11:12 A. L. Jia et al.

Fig. 5. The degree distributions of the interaction graphs of DotAlicious. Straight dashed lines show the

ﬁtted power-law distributions.

are lighter tailed than a power-law distribution. We have found similar results for

interaction graphs of DotAlicious, StarCraft II, and World of Tanks.

Comparison With Regular Online Social Networks: In Section 2, we have classiﬁed

online social networks, including MOGs, into socializing-driven and target-driven net-

works. Here, we compare the differences in their degree distributions.

For friendship graphs, the d egree distribut ions in socializi ng-driven netwo rks such as

Fac ebook and O rkut d o not follo w powe r- law distr ibutions [Mis love et al. 2 007; Wils on

et al. 2009]. In contrast, the degree distributions in many target-driven networks

are found to follow power-law distributions, as shown above for Dota-League, and in

Mislove et al. [2007] for Flickr, LiveJournal, and YouTube.

For interaction graphs, in socializing-driven networks such as Facebook, node degrees

are signiﬁcantly ﬁtted by power-law distributions [Wilson et al. 2009], whereas for

target-driven networks they are not: depending on the number of users involved in a

target, they can be lighter tailed or heavier tailed than power-law distributions. For

example, DotA limits the number of players per game to 10, whereas Meetup allows

thousands of people participate in the same event. As a consequence, we observe that

degree distributions of Dota-League’s interaction graphs are lighter tailed than power-

law distributions, and previous work [Liu et al. 2012] shows that for Meetup, it is

heavier tailed than a power-law distribution.

Moreover, in Dota-League, we observe smaller probabilities for high degree nodes

going from the SM graph to the SS and OS graphs, and further to the MW and ML

graphs. We believe that as the relationship constraints get more restricted (i.e., from SM

to SS and OS, and further to MW and ML), fewer player pairs will pass threshold nand

establish links between them. A similar phenomenon has been found in the interaction

graphs extracted from Facebook [Wilson et al. 2009] and LiveJournal [Mislove et al.

2007].

5.3. The Correlation of Friendship and Interactions

We use the PRCC [Rodgers an d Nic ewander 1988] to mea sur e the correlation between

the number of friends and the number of interactions of a player in MOGs. In brief,

PRCC measures the linear dependence between two variables. We ﬁnd that in Dota-

League, there is a positive correlation between the number of friends in the FR (Friend-

ship) graph and the number of interactions in the SM (Same Match), SS (Same Side),

OS (Opposite Sides), MW (Matches Won together), and ML (Matches Lost together)

graphs, achieving a PRCC of 0.3838, 0.4356, 0.4271, 0.4850, 0.5192, respectively. And

in DotAlicious, as shown in Figure 5, the node degree in general is higher when the SM

graph consists of players with clan membership, compared to the case when all players

are considered. Note that a clan is a self-organized group of players who often form a

league and play on the same side in a match. These results indicate that players with

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:13

strong explicit social relationships, like friendship and clan membership, tend to play

more games.

Further, we ﬁnd from Table II that for Dota-League (DotAlicious), its OS has similar

(smaller) network size than its SS graph, that is, compared to players in Dota-League,

players in DotAlicious are more prone to play on the same side. Possibly due to the clan

feature in DotAlicious, players who often play on the same side are committed to each

other.

5.4. The Inﬂuence of Game Genre

So far, taking DotA, StarCraft II, and World of Tanks as the examples, we have shown

astructuralsimilarityinMOGs:naturallyemergingsocialstructurescenteredaround

highly active players. Nevertheless, as introduced in Section 2, these MOGs repre-

sent different game genres, and therefore, differences in their user relationships are

expected. In this section, we further investigate these game genres.

Alone or Together? As shown in Table II, for the same threshold n=10, while tens of

thousands of players have played in StarCraft II and World of Tanks, their interaction

graphs only contains a few thousands of players, and the fractions of nodes in the LCC

are extremely small. Apparently, StarCraft II and World of Tanks have much fewer

players that would engage in repeated games with same players. Further, as shown in

Table I, StarCraft II and Wor ld of Tanks have larger numbers of players but smaller

numbers of matches compared to Dota-League and DotAlicious, which implies lower

user activities in these two communities.

The aforementioned result also indicates that n=10 is so strict that it ﬁlters out

most player pairs in StarCraft II and World of Tanks. In the following sections, we use

the default values as we chose earlier in Section 4, that is, n=2and4forStarCraftII

and World of Tanks, respectively.

Bonding or Fighting? Comparing the size of the SS and OS graphs, we see that

players tend to play on the opposite side in StarCraft II (83,199 players in its OS graph

versus 25,566 players in its SS graph), on the same side in World of Tanks (15,618

vs. 68,659), and with no strong preference on the playing side in Dota-League (26,373

vs. 24,119). Players in DotAlicious tend to play on the same side (29,377 vs. 11,198),

but the tendency is not as strong as in World of Tanks. We believe this is due to the

clan feature provided by DotAlicious, rather than the game genre. Intuitively, from

RTS to MOBAs and further to MMOFPS games, the requirement of team cooperation

increases, and therefore, players are more likely to maintain an SS relationship with

each other.

Balance or Challenge? Assortativity measures to what extent players link to other

players with similar node degree. As node degree represents player popularity, a pos-

itive assortativity indicates that players with similar popularity often play together,

and a negative assortativity indicates the opposite. We ﬁnd that DotA and World of

Tanks always achieve positive assortat ivities for their S M, SS, and OS graphs, whereas

StarCraft II always achieves negative ones.

The aforementioned result suggests that in games where individualistic skill pre-

vails, for example, RTS games exempliﬁed by StarCraft II, players tend to seek chal-

lenges by playing with popular players. Intuitively, this is an effective way to improve

player skills, since popular players have played with many others so that they po-

tentially attained high skill levels. In fact, we do ﬁnd a positive correlation (with

aPearsonCorrelationCoefﬁcientof0.6191)betweennodedegreeandplayerskill

level in Dota-League, where the skill level is deﬁned based on the fraction of matches

aplayerhaswon.InStarCraftII,teammatesandopponentsareeitherchosenby

players themselves, or assigned by the community based on the similarity of skill

11:14 A. L. Jia et al.

Fig. 6. The fraction of nodes remaining in the LCC as a function of the fraction of the top nodes that are

removed.

levels (see also Section 2.2). Therefore, we attribute the proneness of playing with

highly skilled players in StarCraft II to a player’s willingness to seek challenges.

Overall, our analysis in this section shows that different game designs have differ-

ent inﬂuences on the social relationships emerging among players. For one application,

game designers and MOG community administrators could use our analysis as a refer-

ence to adjust their designs and to maneuver, or manipulate, their players. For example,

our analysis shows that players in StarCraft II tend to seek challenge and compete with

each other (by playing on the opposite side). Administrators of MOG communities that

are similar to StarCraft II can therefore create a competitive environment, for example,

by organizing some tournaments or publishing player ranks, to promote the activity

level of their players and potentially achieve a higher commercial revenue.

We also conjecture that these game gen res v ary i n the e xtent to which playe rs

socialize. However, our data do not allow an analysis on this topic. To do so, we will need

extra information, like how many private messages have exchanged between players.

We consider this an interesting topic for futu re wo rk.

5.5. The Importance of Top Players

In this section, we analyze how the network is connected when top players are removed

gradually. We compare two types of top players, that is, the ones who have many

friends and the ones who have played games with many others, which are identiﬁed

by their node degrees in friendship and interaction graphs. As Dota-League is the only

community for which we have obtained both friendship and interaction information,

we use it as the example.

Previous work [Mislove et al. 2007] has shown that, in some online social networks

where the friendship graphs have power-law distributed node degrees (for example,

YouTu b e ) , r emo v i n g t op nod e s q u ickly b r e a k s the w h o l e g raph a p a r t. Con s i s t ent wi t h

this observation, as shown in Figure 6, the FR graph of Dota-League also breaks down

quickly as more top nodes are removed: with 10% top nodes removed, the fraction of

nodes in the LCC is almost decreased to zero. Further, we observe that interaction

graphs also break down quickly when top nodes are removed. Similar observations in

other online social networks, but not in online games, have been found in Jiang et al.

[2013].

The aforementioned results indicate that top players are important for keeping the

connectivity and holding the whole community together. Community administrators

can adopt special policies to keep the activity of these top players, and therefore, the

activity of the community.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:15

Fig. 7. The seven classes of triads and their ids. Triads 1 to 3 are connected but not closed, and triads 4 to

7areclosed.Thetransitionoftriad1totriad4representsanexampleoftriadicclosure.

Table III. The Fraction of Triads That are Closed in the SS and OS Graphs,

Respectively, of Four MOG Communities

Dota-League DotAlicious StarCraft II Wor ld o f Tanks

SS graph 9.24% 6.62% 2.83% 64.68%

OS graph 7.52% 6.89% 0.17% 3.03%

5.6. Triadic Closure

Aclosedtriadisagroupofthreenodeswhoareconnectedwitheachother.Inpsychology,

it has been shown that triadic closure is more likely to happen with positive rather than

negative relationships, that is, a friend of my friend is likely to be a friend, whereas an

enemy of my enemy is less likely to be an enemy [Heider 1946; Cartwright and Harary

1956]. In this section, we test whether this phenomenon also happens in MOGs.

The prosocial and the enmity relationships are strongly expressed in gaming,

whereas the latter may be repressed in some real-world settings, especially profes-

sional. Therefore, here we consider playing on the same side (SS) as a positive rela-

tionship (represented by “+” in Figure 7) and playing on the opposite side (OS) as a

negative relationship (represented by “−” in Figure 7). In Figure 7, we show the classes

of triads that can happen in MOGs. The transition of triad 1 to triad 4 represents the

triadic closure that may happen in the SS graph. Similarly, the transition of triad 2 to

triad 7 represents the triadic closure that may happen in the OS graph.

In Table III, we show the percentage of triadic closures in the SS and OS graphs

of the four MOG communities we study. We see that Dota-League, StarCraft II, and

World of Tanks achieve higher tria dic closures in their SS graphs than in their OS

graphs. This result conﬁrms that triadic closure is more likely to happen among positive

relationships, that is, playing on the same side. For DotAlicious, we ﬁnd similar triadic

closures for its SS and OS graphs. One possible reason is that the clan feature provided

in DotAlicious diminishes the signiﬁcance of playing on the opposite side being a

negative relationship. It remains for future work on other datasets to establish whether

our conjecture is valid.

5.7. Social Balance

The social balance theory reveals a phenomenon that is often observed in signed graphs,

that is, graphs with a “+”or“−” sign for each link. In this theory, a triad is deﬁned

as positive (balanced) if the product of the signs of its links is positive, and negative

(unbalanced) otherwise. The social balance theory claims that balanced (unbalanced)

triads in social networks should be over (under) represented compared to random

graphs [Heider 1946; Cartwright and Harary 1956; Heider 1944]. In this section, we

test the social balance theory based on our data.

11:16 A. L. Jia et al.

Table IV. The Number and the Percentage of Class 4 to Class 7 Triads (as shown in Figure 7) in the Original

Signed Graph (

N

!)andintheRandomSignedGraph(

N

rand

!), Respectively

Triad id Class 4 triad Class 5 triad Class 6 triad Class 7 triad

Dota-League N"297,495 (8.98%) 1,078,516 (32.56%)1,341,609 (40.50%)594,991 (17.96%)

Nrand

"353,745 (10.68%) 1,172,524 (35.40%)1,302,035 (39.31%)484,307 (14.62%)

DotAlicious N"364,475 (9.37%) 1,198,269 (30.82%)1,592,434 (40.95%)733104 (18.85%)

Nrand

"548,411 (14.10%) 1,514,709 (38.96%)1,395,471 (35.89%)429,691 (11.05%)

StarCraft II N"16,551 (10.12%)5,344 (3.27%)130,494 (79.72%)11,216 (6.86%)

Nrand

"2,060 (1.26%)19,625 (12.00%)66,291 (40.52%)75,629 (46.23%)

World of Tan ks N"1,217,812 (18.85%)407,918 (6.32%)4,677,089 (72.41%)156,396 (2.42%)

Nrand

"1,217,812 (12.5%)3,653,436 (37.50%)3,653,436 (37.50%)1,217,812 (12.50%)

The results shown in the bold font represent cases that follow the social balance theory.

For each of the four MOG communities, w e ﬁrst combine its SS a nd OS graphs into

one signed graph, which we call the original signed graph. Then, we randomize the

sign of each link in this signed graph to generate a random signed graph.Notethat

the random signed graph keeps the same fractions of “+”and“−”signs,andthesame

graph structure as the original signed graph. Therefore, our following analysis on social

balance will not be inﬂuenced by the graph structure.

To test the social balance t heory, we con sider the four classes of closed triads (triads

4 to 7) as shown in Figure 7. In Table IV, we show the number and the percentage of

class 4 to class 7 triads in the original signed graph and in the random signed graph,

represented by N"and Nrand

",respectively.Theresultsinboldfontrepresentcases

that follow the social balance theory, that is, balanced (unbalanced) triads in social

networks should be over (under) represented compared to random graphs.

We see that the social balance theory holds in most cas es, except for triad s 4 and 7 i n

Dota-League and DotAlicious. Recall that Table III shows that, compared to StarCraft

II and World of Tanks, Dota-League and DotAlicious also have more similar percentages

of triadic closure for their SS and OS graphs. These results suggest that while the

social balance theory holds for most MOG communities, the signiﬁcance of SS being a

positive relationship and OS being a negative relationship varies across different MOG

communities.

Szell and Thurner [2012] have also observed a similar social balance phenomenon in

an MOG named Pardus.Nevertheless,intheiranalysis,thepositiveandthenegative

relationships are identiﬁed by users, while in our analysis they are revealed explicitly

by user interactions.

6. BEHAVIORAL CHANGE AND NETWORK EVOLUTION

In Sections 4 and 5, we have always considered the whole datasets. For Dota-League, it

contains user interactions from November 2008 to February 2012. Obviously, players

may change their interaction patterns, and therefore, the network evolves over time.

In this section, we study user behavioral change and network evolution in MOGs.

6.1. Two Models for Network Evolution

In this section, we propose two models for analyzing network evolution in MOGs.

Existing network evolution models are insufﬁcient for our analysis, for two reasons.

First, they are mostly based on friendship [Garg et al. 2009; Kairam et al. 2012;

Hu and Wang 2009], whereas we consider more dynamic relationships, that is, user

interactions. Secondly, a few models [Viswanath et al. 2009; Leskovec et al. 2005;

Merritt and Clauset 2013; Ribeiro et al. 2013; Caceres and Berger-Wolf 2013] do include

user interactions, but they only consider one perspective on network evolution, whereas

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:17

we differentiate and compare two types of network evolution, network dynamics and

network growth.

Without this comparison, contradicting conclusions can be drawn from the incom-

plete analysis. For example, researchers in Leskovec et al. [2005] have proposed a

densiﬁcation law, which states that many social networks densify over time, with the

number of edges growing superlinearly in the number of nodes. And researchers in

Merritt and Clauset [2013] contradicted this ﬁnding by showing that the friendship

network they examined is nondensifying. The problem is that they have considered

different types of network evolution. And as we will show later, depending on the evo-

lution models, both densiﬁcation and nondensiﬁcation can happen even for the same

network.

We deﬁne the periodic graphs of a network for a certain time duration as the sequence

of graphs obtained by only considering those user interactions that have occurred in

the successive periods of that duration—one can think of a periodic graph of a network

as starting at the beginning of the corresponding period without any edges, and with

only edges added for interactions that occur within the speciﬁc period. In contrast, the

cumulative graph of a network up to a certain point in time has edges for all interactions

that have ever occurred up to that time. We consider the periodic and the cumulative

graphs to capture network dynamics and network growth, respectively. Under both

models, we examine the network periodically based on a predeﬁned checkpoint interval

(the length of the period). At each checkpoint, we generate a periodic graph from

the interactions that happened within the corresponding interval, and we generate a

cumulative graph based on all the interactions that happened before that checkpoint.

Previous work on network evolution that comes closest to our analysis is [Krings et al.

2012], in which the authors examined the effects of time window size (corresponding

to the checkpoint interval in our approach) and placement (which decides whether it

is a cumulative or a periodic graph in our approach) on the structure of aggregated

networks. Nevertheless, they only consider one type of interaction, that is, phone calls,

and they assume a link exists between two users as long as they have interacted before,

regardless of their interaction strength. In contrast, as introduced in Section 3.2, we

consider different types of interactions, and we use threshold n(which reﬂects the

interaction strength) to decide whether links should be added between players. We

also analyze the inﬂuence of non the network evolution models.

In our analysis, for each of the four MOG communities, we consider the aforemen-

tioned two models with three checkpoint intervals, that is, one week, one month, and

half a year, and two interaction thresholds, that is, n=1andn=10. In total, we gen-

erate 12 sets of graphs for each community (two types of evolution, three checkpoint

intervals, and two thresholds), and each set consists of ﬁve interaction graphs (SM,

SS, OS, MW, and ML graphs). In general, we observe similar patterns for the network

evolution of the interaction graphs in these communities, and therefore, we only show

the results for the SM graph of Dota-League in Figures 8–10.

6.2. Network Dynamics Versus Network Growth

For the cumulative graph s, regardless of the checkpoint interval, the network size

[Figure 8(a)], the number of links [Figure 8(b)], and the average node degree [Fig-

ure 8(c)] increase over time, indicating that the whole network is getting denser. We

also observe from Figure 8(d) that after a short period of increase, the diameter of LCC

actually decreases over time. Similar phenomena in network growth, that is, network

densiﬁcation and shrinking diameter,havebeenobservedinmanyothernetworksas

well [Leskovec et al. 2005].

While the cumulative graphs seem to demonstrate the prosperity of the network, the

periodic graphs show different, or even opposite trends in the network. We see from

11:18 A. L. Jia et al.

Fig. 8. Network evolution: cumulative graphs (checkpoint interval equal to one month, n=10).

Fig. 9. Network evolution: periodic graphs (checkpoint interval equal to one month, n=10).

Figure 9(a) and 9(b) that, after a short period of increase (within the ﬁrst ﬁve months),

the network size and the number of links in fact decrease over time, indicating that

as time evolves, the whole network becomes less active. This is partially due to the

decreasing popularity of Dota-League, which eventually led to its shut down in 2012.

Meanwhile, we observe that the increase of the node degree and the decrease of the

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:19

Fig. 10. Network evolution: the special case of the ﬁrst half year (checkpoint interval equal to half year or

one month, n=10).

diameter over time are more obvious in the cumulative graphs (Figure 8) than in the

periodic graphs (Figure 9).

The aforementioned results indicate that the understanding of network evolutions

depends signiﬁcantly on the network evolution model, and a clear deﬁnition of network

evolution is crucial for understanding the network.

6.3. Committed Early Members

As shown in Figure 10, for both evolution models, the ﬁrst half year (i.e., 6 months

and around 24 weeks) is a very special case. Compared to the rest of the data, it has

the smallest network size and the smallest LCC size [Figure 10(a) and 10(b)], yet

it achieves the highest clustering coefﬁcient [Figure 10(c) and 10(d)]. Intuitively, one

would expect a higher clustering coefﬁcient for the graph with a smaller network size,

simply because there will be fewer nodes to choose at endpoints. However, we observe

that in the ﬁrst half year, both the network size [Figure 9(a)] and the average clustering

coefﬁcient [Figure 10(f)] increases with time. These results show that in the early days,

11:20 A. L. Jia et al.

Fig. 11. Network evolution: the inﬂuence of threshold n(periodic graphs, checkpoint interval equal to one

month, n=1).

though Dota-League had not attracted as many players as it later did, players were

connected more closely then, than later. We conjecture that this phenomenon—in the

early days, members are often more committed to the community—also happens in

many other online and ofﬂine communities.

6.4. The Inﬂuence of Threshold

n

We have also test ed th e cas e of n=1forourmodelsusingDota-LeagueSMgraph

as the example, and we observe a similar trend of network evolution as in the case of

n=10. As an example, Figure 11 shows the network size and the average node degree

for our periodic graph model. The case for n=10, which requires a different scale, is

depicted in Figure 9. Similar to the case of n=10, we observe that after the ﬁrst six

weeks, the network size decreases and the node degree increases slightly over time.

This result indicates that the threshold ninﬂuences mostly the scale of the evolution,

but not the trend.

7. SOCIAL RELATIONSHIP AND MATCH RECOMMENDATION

Taking match recommendation as the exampl e, in this section, we study t he implica-

tions of our model on gaming services.

7.1. Overview

Match recommendation in an MOG community predicts player pairs that are likely

to form gaming relationships in the future, such as playing together, playing on the

same and/or the opposite sides. Match recommendation often includes two types of

predictions, that is, predicting new relationships between players who previously had

no relationships at all, and predicting repeated relationships between players who have

formed the same relationships in the past.

Good match recommendation algorithms help improve user experience, and hence,

the commercial value of MOGs. However, they are often neglected or seem to have

been only casually designed. For example, in Dota-League, players can only join a

waiting queue, and, only when there are enough players, teams are formed considering

the skill levels of the players in the game. Although this algorithm enforces balanced

matches, it does not take into account the social relationships of players. As a possible

consequence, we observe that 41% of the games in Dota-League are aborted at the

very beginning of the match. Moreover, deﬁcient matchmaking algorithms, for exam-

ple, those solely based on skill, are likely to be subject to user manipulation [Caplar

et al. 2013]. Given the aforementioned reasons, in this section, we study the match

recommendation problem in MOGs.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:21

Predicting new relationships is in fact a form of the link prediction problem,which,

given a snapshot of a network, seeks to accurately predict links that will be added to

the network in the future [Liben-Nowel and Kleinberg 2003]. In this section, we will

assess the performance of traditional link-prediction algorithms, with some variations

based on our models, for predicting new relationships in MOGs. Combining the tasks

of predicting new and repeated relationships, we also propose SAMRA, a Socially

Aware Match Recommendation Algorithm that takes social relationships revealed by

our model into account. We show that our model not only improves the precision of

traditional link prediction approaches, but also, via a domain-speciﬁc metric derived

from gaming studies [McGonigal 2011], potentially helps players enjoy the game to a

higher extent.

7.2. Link Prediction Approaches Applied to MOGs: Predicting New Relationships

In this section, we will assess the performance of traditional link-prediction algorithms

for predicting new relationships in MOGs.

7.2.1. Link-Prediction Algorithms.

To predict new links, a link-prediction algorithm ﬁrst

calculates the similarity between nodes. Assuming that similar nodes are more likely

to establish new links, it then produces a list of potential new links. The deﬁnition of

similarity varies across algorithms. For our analysis, we consider the following four

popular algorithms.

Common Neighbors. The idea behind this algorithm is that the larger the intersection

of the neighbor sets of any two nodes, the larger the chance of future interactions

between them [Liben-Nowel and Kleinberg 2003].

Adamic/Adar. This algorithm also measures the intersection of neighbor sets of a

user pair, but emphasizes a smaller overlap [Adamic and Adar 2001].

Katz Measure. The rationale behind this algorithm is that the more paths exist

between any two nodes and the shorter these paths, the larger the chance of future

interactions between them [Katz 1953].

Rooted PageRank. This algorithm captures the probability of random walks starting

from two nodes in the graph to meet each other, and uses this probability to quantify

the chance of future interactions between them [Song et al. 2009].

7.2.2. Experiment Setup.

As link predictions are often needed within a short time span,

we take one year worth of data of Dota-League, from March 2011 to February 2012,

as the example to test the performance of link-prediction approaches on match rec-

ommendation. First, we divide the data into two parts, the training and the testing

data. Next, we generate two sets of interaction graphs based on interactions observed

in the training and testing data, indicated by SM1 and SM2 (Same Match), SS1 and

SS2 (Same Side), and so on, respectively. Then, we run a link-prediction algorithm on

the training data, which produces a list of predicted links ranked in decreasing order

of prediction conﬁdence. Finally, we take the set PNof top-Nlinks from this prediction

list and we check whether these links indeed occur in the testing data. Indicating the

set of links in the testing data by L2,weuseprecision deﬁned as |PN∩L2|/|PN|as the

metric to measure the performance of top-Nlink prediction.

We have test ed di ffe rent partitionings of the data, and we have f ound that using the

ﬁrst half year as the training data and the second half year as the testing data gives the

best prediction performance. We use this partitioning for all the following experiments.

Under this partitioning, the number of new links in the testing data as compared to the

training data for the SM, SS, OS graphs are 66,612, 18,912, and 25,340, respectively.

7.2.3. Unitary Prediction and Hybrid Prediction.

We call predictions based on the same type

of interactions for training and testing unitary predictions, and predictions based on

11:22 A. L. Jia et al.

different types of interactions hybrid predictions. Traditional link predictions are often

unitary, for example, using links in SM1 to predict links in SM2. As our model captures

different types of interactions, it provides the opportunity for hybrid predictions. For

example, matches won together (MW) often generate a strong social attachment and

players who have won together are very likely to play on the same side (SS) in the

future. Thus, it may be beneﬁcial to use links in MW1 to predict links in SS2.

7.2.4. Results.

Here, we consider ﬁve types of relationships, that is, SM (Same Match),

SS (Same Side), OS (Opposite Side), MW (Matches Won together), and ML (Matches

Lost together). As discussed in Section 4, we use n=10 as the default value to generate

the interaction graphs from the training and the testing data. We focus on two predic-

tion tasks, that is, predicting player pairs that will play on the same (SS) and opposite

sides (OS). Note that the precision of predicting the SS and the OS relationships are

in fact lower bounds for the precision of predicting the SM relationship. We use both

unitary and hybrid predictions for these tasks. In Figure 12, we show the precisions of

these predictions, from which we obtain the following observations.

First, we see that among the four link-prediction algorithms we consider, there are no

dominant algorithms that outperform the others for all cases. This result is consistent

with previous work [Liben-Nowel and Kleinberg 2003] on evaluating the performance

of link-prediction algorithms. Secondly, we ﬁnd that in general, for any link-prediction

algorithm, a higher value of Nleads to a smaller precision, since the predicted links

are ranked in decreasing order of prediction conﬁdence. Thirdly, we observe that the

predictions based on MW1 and ML1 perform better than the predictions based on SS1

and OS1, which in turn perform better than the predictions based on SM1. We believe

the reason is that, as we use the default value n=10 for generating the these graphs,

the relationships presented in MW1 and ML1 are stronger (i.e., less casual) than in

SS1 and OS1, which in turn are stronger than in SM1. For the gaming datasets we

study, the relationships inferred from strong relationships in the past are more likely

to happen in the future.

Further, we ﬁnd that predictions based on SS1 perform better than predictions based

on OS1. We observed earlier in Section 5.6 that for Dota-League, triadic closure is

more likely to happen for the SS relationship than for the OS relationship. These

results suggest that the SS is less casual than the OS relationship. On the other hand,

predictions based on MW1 and ML1 achieve similar performance. One possible reason

is that in Dota-League, winning and losing together do not have signiﬁcantly different

impacts on user relationships.

7.3. Beyond Precision and Link Prediction

In the previous section, we have assessed the performance of link prediction to the

match recommendation problem based on the well-known metric of precision. This

analysis does not completely solve the match recommendation problem, for two reasons.

First, precision alone is not sufﬁcient for measuring recommendation quality, since

the actual new links in the testing data are affected by the current recommendation

algorithms. If a player did not play with recommended players in the period of the

testing data, it may be because the current system did not introduce them and the

player did not know about the possibility of playing with these players, and not because

the recommendation is of low quality. Therefore, we need new metrics beyond precision.

Secondly, traditional link-prediction algorithms can only predict new relationships.

Match recommendation, on the other hand, requires predicting both the new and the

repeated relationships. For the latter case, we need new algorithms that go beyond link

prediction.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:23

Fig. 12. The performance of link-prediction algorithms for match recommendation (horizontal axis with

logarithmic scale).

Our approaches to solve the aforementioned two problems are discussed in the fol-

lowing two sections.

7.4. Bonding Score: A Prosocial Metric for Online Games

To solve the ﬁrst problem in Section 7.3, we prop ose a new metric for me asuring match

recommendation quality called the bonding score,whichtakesthesocialcomponents

in games into consideration. There are multiple ways to deﬁne bonding score. Never-

theless, our goal is not to propose a unique scoring method, but rather to show how

11:24 A. L. Jia et al.

Fig. 13. The CDF of component size for different values of interaction threshold n(Dota-League, SM graph).

Fig. 14. An example of a match with a bonding score of 7.

to compare and possibly improve match recommendation based on one such socially

aware scoring system.

To do so, we consider the ﬁndings of McGonigal [2011], who have pointed out that

matches played by players with strong social ties are enjoyed to a higher extent than

those played amongst players that have weak or no social ties. In our model, identifying

strong social ties amounts to increasing the threshold nof the number of interactions.

As we have shown in Figure 1, when nincreases, the fraction of nodes in the LCC

decreases dramatically. We further show in Figure 13 the CDF of the component size

in Dota-League’s SM graph, for different values of the threshold n.Weseethat,when

nincreases, players are grouped into small, intensely interacting components. For

example, when n=10, less than 10% players are outside the LCC, while when n=100,

more than 90% players are outside the LCC and form connected components with sizes

smaller than 40.

We calculate the bonding score of a match of two teams in the following way. Fir st, w e

generate the interaction graph for the interaction type we are interested in based on a

large value of the threshold n,sothatonlystrongtiesarepresentinthegraph.This

interaction graph consists of a number of connected components. Then, we calculate

the overlap of components across the players of both teams: a match receives one score

point for every player (of any of the two teams) who is in a connected component that

is represented in the match by at least two players (again, of any of the two teams).

As an example, consider the match between the two teams shown in Figure 14. Here,

Components 1, 2, and 3 have more than one player in the match, namely players a

and c in Component 1, players b and f in Component 2, and players d, h and j in

Component 3, respectively. Therefore, the bonding score of this match is equal to 7.

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:25

Fig. 15. The average bonding score of all Dota-League matches, for random recommendation, the original

recommendation algorithm used in Dota-League, and SAMRA. We use n=10 to generate the interaction

graphs from the training data.

7.5. SAMRA: A Socially Aware Match Recommendation Algorithm

To solve the second p roblem introduc ed in Section 7.3, we propose a Socially Aware

Match Recommendation Algorithm (SAMRA), which takes the bonding score into con-

sideration.

In SAMRA, ﬁrst, for each 10min time interval,3we build a list of all the players

who are online and have not yet been assigned to a match. Secondly, for each of these

online players, we compute their connected components based on the interaction graphs

extracted with a large value for threshold n.Thirdly,werankthesecomponentsin

decreasing order of their size, and from the top to the bottom of this ranking, we

assign all online players from the same component to the same match if size permits;

otherwise we split the component into a number of parts, with the number of players

in each part equal to the match size, who then are assigned to the same match.

We test the performance of the SAMRA using both the bon din g sco re an d the p re-

cision. We set n=100 to generate the interaction graphs based on which our match

recommendation algorithm works. The online time of users and the duration of matches

are obtained from the original data.

7.5.1. Performance: Bonding Score.

First, we compare the bonding scores obtained via

SAMRA with those observed in practice. For comparison, we have also scored the

matches obtained via random matching. We use the Dota-League dataset as the ex-

ample. The results are shown in Figure 15. We see that SAMRA, albeit simplistic, can

reach higher match bonding scores than its nonsocial counterparts. We attribute this

improvement to the difﬁculty of seeing whether friends are online in real systems due

to shortcomings in the offered matchmaking methods. We have tested different values

of nand we have obtained similar results.

7.5.2. Performance: Precision.

Here, we test the precision of SAMRA for predicting new

relationships and repeated relationships, respectively.

Predicting New Relationships: Using the same training and testing data as in

Section 7.2, we calculate the precision of SAMRA in predicting new relationships, that

is, the percentage of player pairs it recommends that indeed occur in the future. We

compare SAMRA with traditional link-prediction algorithms exempliﬁed by Common

Neighbors.

As we use n=100 to generate the interaction graphs based on which SAMRA works,

to have a fair comparison, for the Common Neighbor method, we use n=100 to generate

the interaction graphs from the training data as well. (Recall that in Section 7.2 we

3Most matches in Dota-League last for around 40min. Therefore, 10min intervals provide enough granularity

for capturing most of the online sessions.

11:26 A. L. Jia et al.

Fig. 16. The precision of SAMRA and Common Neighbors in predicting new relationships (horizontal axis

with logarithmic scale). To have a fair comparison, for the Common Neighbor method, we use n=100 to

generate the interaction graphs from the training data.

used n=10 as the default value.) We consider the same prediction tasks as in Section

7.2, that is, predicting the SS and OS relationships, and we focus on unitary predictions.

The results are shown in Figure 16.

We see that Common Neighbors achi eve a b etter top- Nprecision for a smaller value

of N(i.e., N<250) while SAMRA performs better for a larger value of N(i.e., N>250).

As Common Neighbors ranks predicted links based on prediction conﬁdence, when N

increases, the decrease of its precision is more skewed compared to SAMRA.

Predicting Repeated Relationships: As link-prediction algorithms are not able to

predict repeated relationships, here we only show the results of SAMRA. For the task

of predicting repeated SS and OS relationship, we ﬁnd that SAMRA achieves precisions

of 60.60% and 65.88%, respectively.

We have tested di ffe ren t val ues of nfor generating interaction graphs based on

which SAMRA works. Consistent with our intuition, the choice of nimposes tradeoffs

on the recommendation performance: a larger value of nextracts stronger relationships

that will help our recommendation algorithm to achieve better precision, but on the

other hand, it also excludes players that are without strong relationships and for these

players it cannot make any recommendation. Therefore, in general, a larger value of n

yields a higher top-Nprecision when Nis small and a lower top-Nprecision when N

is large. Depending on the design philosophy, MOG community administrators could

use large values of nto emphasize the prediction precision or small values of nto cover

most of their users.

8. RELATED WORK

In this paper, we propose graph models to analyze social relationships and network

evolutions in Online Multiplayer Games (MOGs). We further use match recommen-

dation as the example to show the application of our models to gaming services. We

summarize related work within each research topic as follows.

Graph Models in Regular Online Social Networks. An increasing number of social

network analyses adopts the complex network approach, that is, using graphs to rep-

resent user relationship. A comprehensive overview of research on complex networks

can be found in Newman [2003]. Some previous work considers only static relationship

like friendship [Garg et al. 2009; Kairam et al. 2012; Hu and Wang 2009; Mislove

et al. 2007]. In contrast, we consider user interactions that are more dynamic. Some

previous work like [Wilson et al. 2009; Viswanath et al. 2009; Leskovec et al. 2005;

Xiang et al. 2010; Liu et al. 2012] has also considered user interactions. However, in

their approaches graphs are extracted based on a single, domain-speciﬁc, and usually

threshold-based rule for mapping interactions to links. Choudhury et al. [2010] have

analyzed the inﬂuence of thresholds on graph properties. Nevertheless, they have only

considered one type of threshold, that is, the number of interactions (equivalent to n

Socializing by Gaming: Revealing Social Relationships in Multiplayer Online Games 11:27

used in our paper), and one type of interaction, that is, email exchange. In contrast,

in this paper, we conduct a sensitivity study of various thresholds and rules based on

different types of interactions.

Graph Models in MOGs. Within MOGs, Kirman and Lawson [2009] proposes a graph

model in which interactions are simply considered as homogeneous and are mapped

to undirected and unweighted links. Merritt and Clauset [2013] considers the number

of interactions when forming the links, but they still consider interactions as homoge-

neous. Existing work is complemented by considering and comparing friendship and

enemy relationships [Szell and Thurner 2012], but they still do not differentiate inter-

actions with various types and strengths. In Ang [2011], differences in graphs extracted

based on different types of interactions are studied, but their dataset is rather small,

with only 74 users involved, whereas our datasets in this paper cover millions of users.

In Balint et al. [2011] and Posea et al. [2010] several graph extraction strategies are

investigated, but they do not form a formalism as comprehensive as we propose here.

Our previous work [van de Bovenkamp et al. 2013; Iosup et al. 2014] propose graph

models to analyze social relationships in MOGs, but they lack a thorough study of

the impact of mapping functions and thresholds on the characteristics of the resulting

graphs.

Network Evolution Models. Most previous works on network evolution only consid-

ers static relationships such as friendship [Garg et al. 2009; Kairam et al. 2012; Hu

and Wang 2009], where the deletion of links are rare and therefore, networks are

expected to grow. In contrast, we focus on more dynamic relationships, that is, user in-

teractions. A number of previous works have considered interactions [Viswanath et al.

2009; Leskovec et al. 2005; Merritt and Clauset 2013; Ribeiro et al. 2013; Caceres and

Berger-Wolf 2013], however, they can be arbitrary when deﬁning network evolution and

they often consider only one of the two types, network growth and network dynamics.

Instead, we consider both of them and we analyze their differences.

Previous work on network evolution that comes closest to our analysis is [Krings

et al. 2012], in which the authors have analyzed both the network growth and the

network dynamics. Nevertheless, they only consider one type of interaction, that is,

phone calls, and they assume a link exists between two users as long as they have

interacted before, regardless of their interaction strength. In contrast, we consider

different types of interactions, and we use threshold n(which reﬂects the interaction

strength) to decide whether links should be added between players. We also analyze

the inﬂuence of non the network evolution models, as well as on the predictions made

by the models.

Applications. Besides understanding the nature of the network, graph models are

useful in many applications, including regenerating and predicting the evolution of

the network [Garg et al. 2009; Kairam et al. 2012; Leskovec et al. 2005], analyzing

information diffusion [Liu et al. 2012], and exporting trustworthy user relationships

to social-based distributed applications like Reliable Email and SybilGuard [Wilson

et al. 2009]. In this paper, we use match recommendation as the example to show the

application of our models. We complement our previous work [van de Bovenkamp et al.

2013; Iosup et al. 2014] by showing how our models not only improve the traditional

link prediction approaches, but also potentially help players enjoy games to a higher

extent.

9. CONCLUSION

MOGs have attracted hundreds of millions of players world-wide among whom rich

social relationships have developed. With traditional complex network approaches and

extensive datasets from three MOGs that contain in total years of behavioral history

for millions of players and games, in this paper, we are able to propose and evaluate

11:28 A. L. Jia et al.

a graph model that captures a variety of social relationships in MOGs. Among many

interesting observations, we ﬁnd that MOGs quickly become disconnected when the

constraints for relationships to exist increase, that friendship has a positive inﬂuence

on user interactions, that MOGs can exhibit growth even when their player activity

declines, and that members in the early days of MOGs are often more committed to

the communities. Taking match recommendation as the example, we further study the

implications of our model on gaming services. We propose SAMRA, a socially aware

match recommendation algorithm that takes social relationships into account. Results

show that our model not only improves the precision of traditional link prediction

approaches, but also potentially helps players enjoy the games to a higher extent.

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Received May 2014; revised October 2014; accepted February 2015