Signed Social Networks: A Survey
Nancy Girdhar and K. K. Bharadwaj
School of Computer and Systems Sciences,
Jawaharlal Nehru University, New Delhi-110067, India
Abstract. People hold both sorts of emotions-positive and negative against each
other. Online social media serves as a platform to show these relationships,
whether friendly or unfriendly, like or dislike, agreement or dissension, trust or
distrust. These types of interactions lead to the emergence of Signed Social
Networks (SSNs) where positive sign represents friend, like, trust, agreement
and negative sign represents foe, dislike, distrust and disagreement. Although
an immense body of work has been dedicated to the field of social networks;
the field of SSNs remains not much explored. This survey first frames the con-
cept of signed networks and offers a brief discourse on the two most prevalent
theories of social psychology applied to study them. Then, we address the vari-
ous state-of-the-art issues which relates the real world scenarios with signed
networks. Grounded along the network attributes, this survey talks about the
different metrics used to analyze these networks and the real world datasets
used for observational purposes. This paper, makes an attempt to follow the
contours of research in the area to provide readers with a comprehensive under-
standing of SSNs elaborating the open research areas.
Keywords: Signed Social Networks, Structural Balance Theory, Status Theory,
One of the intrinsic potential benefits of social media is that one can take a deep in-
sight in one’s life as people are using it as a platform to open up with their opinions,
emotions, thoughts and their beliefs on various topics on the web. They can express
their views in various forms by liking or disliking as different people have different
opinions on a particular topic. So, in addition to the concept of trust, support and
friendship, these social interactions can also reflect disagreements and conflicts
among the people on the social media sites. Thus, it is significant to take into consid-
eration the hostile relations (negative links) along with the friendly associations (posi-
tive links) between the users. The social networks having information about the type
of links (positive or negative) among the users besides the links itself are termed as
Signed Social Networks (SSNs).
Although, a plethora of approaches is dedicated for the analysis of social networks
(SNs); however most of them consider these networks as having only friendly (posi-
tive) relationships while ignoring the hostile (negative) ones entirely. The increase in
the number of users on social networking sites as well as information about the posi-
tive and negative relationships among them has driven the researchers towards inves-
tigating the accountabilities of these relationships in the mining of social network
data. Many research works ,  have encountered a significant change in the
nature and complexity of social graph, once the negative links are introduced in the
networks. This lays the foundation for utilizing the negative links in various applica-
tions such as link prediction , , , , , recommender systems ,
 and community detection [1, 2], , . Therefore, these SSNs are recently
grabbing inexorable attention from the research community. This article reviews the
various state-of-the-art issues of SSNs.
The rest of the article is organized as follows: Section 2 gives a brief on the back-
ground details of SSNs. Section 3 describes the state-of-the art and Section 4 discuss-
es the datasets and evaluation metrics used for analyzing signed networks. Finally, the
Section 5 presents some future research directions along with the conclusion.
According to Moshirpour , Signed Networks are defined as the extension of
networks that include the additional information about positive and negative links.
Signed Social Network: Mathematically,  a directed signed social network
represented as signed graph can be defined as where, is the vertex set
representing nodes of the network, is the edge set that represents the links
of the network and is a function which assigns value if
there is a positive link (friend/trust) from node to node , is assigned if there is
a negative (foe/distrust) link from node to node and if there is no link between
the two nodes .
For example: Let a signed network having users U1U2, U3, U4, U5 is
represented by a directed graph and is the corresponding adjacency matrix as
shown in Fig. 1. Here, a friend (positive) relation is shown with a green color edge
and a foe (negative) relation is represented with a red color edge.
U1 U2 U3 U4 U5
Fig. 1. Graphical representation of a Directed SSN
Ignoring the direction of the signed links, the network can be converted into undi-
rected network assuming the links between the nodes as bidirectional and thus, the
adjacency matrix representation of the undirected network will be symmetric in na-
2.1 Theories of Signed Networks
To analyze these online SSNs there are two different theories . A brief descrip-
tion of each of these theories is given as follows
Structural Balance Theory is the fundamental theory formulated by Heider in
1946 . Based on the concept of Friend-of-a-Friend (FOAF), this theory is a no-
tion to understand the structure, cause of tensions and conflicts between the two sen-
timents (positive and negative) in a network of actors (users). Further, Cartwright and
Harrary in 1956  modeled it in terms of signed graphs. This theory rests on the
assumption that certain configurations of positive and negative edges are socially
more probable than others. Ignoring the identities of the actors, four configurations
are possible: “my friend’s friend is my friend”, “my friend’s enemy is my enemy”,
“my enemy’s friend is my enemy”, “my enemy’s enemy is my friend”.
According to the structural balance theory, a balanced triad is one with either one
or three positive links (i.e., odd number of positive links) among three people. In Fig.
2, the first two triads are balanced as they have an odd number of positive links while
later two are unbalanced as they have even number of positive links. This theory is
pertinent on undirected networks only.
Fig. 2. Various Configurations of Social Triads
Social Status Theory suggested by Guha et al.,  and further developed by Lesko-
vec et al.,  proposes to use status of a person as the factor to decide whether a
person will make a link (positive or negative) with another person in the network.
Status can be in terms of social status (popularity, fame) or it can be economical sta-
tus (money, power). Pagerank is one of the most popular ways to calculate status
score in social networks.
According to this theory, if individual (creator) makes a positive link to individ-
ual (recipient), then believes that has higher status than him, whereas a nega-
tive link originated from individual to indicates that considers status of low-
er than him. It is evident that the status theory is more suitable for directed networks.
To check whether triads of a network satisfy status theory, take each negative link in a
triad, inverse its direction and the flip the sign of the link (positive sign) then the re-
sultant triad should be acyclic in nature.
Computation of Status of a node: The status of a node in a directed network
can be computed  as follows:
denotes the number of positive and negative links re-
ceived by the node from other nodes in the network respectively. Similarly,
is the number of positive and negative links generated by the node in
the network, respectively.
Balance Theory vs Status Theory: In order to sense the difference between bal-
ance theory and status theory, assume the case that node connects negatively to
node , further node connects negatively to node . Now what will be the sign of
the link connecting node to node ? Considering balance theory’s configuration
“My enemy’s enemy is my friend”, predicts the sign of the link between and as
positive, whereas, the status theory predicts the sign of the link from to as nega-
tive. In other words, the result of balance theory differs from the results of status theo-
ry in this case.
3 State-of –the-art
Link Prediction in SSNs: Traditional link prediction approaches used for social
networks are massively based on the concept of “friendship”. Thus, neglecting the
other side of relationships viz., antagonism. Users in these networks find it difficult to
decide among the people they trust from those they don’t. Thus, they find it vague and
obscure to distinguish between a friend and an acquaintance , . Therefore,
these approaches are not well suitable for analyzing and predicting links in SSNs.
Recently, researchers have begun to investigate on how to turn an unsigned ac-
quaintances network into signed trust/distrust network , , . A variety of
available networks like Epinions, Slashdot, Wikipedia etc. have also started labeling
links explicitly either as friend/foe  or trust/distrust , . A number of theo-
ries in sociology ,  provide deeper insight into the fundamental principles
which explain how the patterns of negative and positive links resulted into different
kinds of relationships. According to structural balance theory , , people in
signed networks ,  tend to follow the notion of FOAF whereas, status theory
is based on the concept of social status which people possess in a society.
Thus, the sign inference problem, which aims to infer the unknown relationship be-
tween two entities, can be achieved by learning from balance or status information of
Community Detection (CD) in a social network is identification of set of nodes
that are more densely connected to each other than to the rest of the network , .
Different approaches in the literature are proposed to tackle the problem of com-
munity detection in social networks. Some traditional clustering algorithms assume
communities as disjoint structure, where as some approaches assume communities as
overlapping structures in the real-world networks . Graph partitioning algorithms
, hierarchical clustering algorithms  have also been used for CD in social net-
works etc. As CD in signed social networks is a bit different from the CD in social
networks, its definition should take into account the extra information about the type
of links among the users besides the links itself which is stated as follows:
Community Detection in SSNs attempts to partition the network in such a way
that each partition should have dense positive intra-connections and sparse negative
intra-connections. One way to do such optimization is by using the concept of modu-
larity introduced by Newman .
Trust, Distrust and Reputation in Community Detection: In recent few years a
lot of work is done on trust and reputation. Trust and distrust are personal characteris-
tics while reputation is a public characteristic of a person/organization. Trust and
reputation are very necessary components in real world social networks and these are
incorporated in most of the domains like recommender systems , , e-learning,
e-commerce, semantic web and so on.
Recently, researchers have begun to scrutinize on how to transform an unsigned
social network into signed trust/distrust network , , , . A variety of
existing networks have also started tagging links explicitly either as friend/foe  or
trust/distrust  (like Epinions, Slashdot, Wikipedia). To bring any online model or
network more near to the physical world, it is inevitable to incorporate trust and repu-
tation in it.
Social Recommender Systems: The principle intent of Social Recommender Sys-
tems (SRSs) is to ease information overload over social media users by delivering the
most attractive and relevant content/items they are looking for. SRSs that suggest
content, people and communities often used personalization techniques  to adapt
the needs and interests of an individual user or a group of users. There is a lot of work
done both in industry and academia for developing new approaches in recommender
systems over the last decade.
In SSNs, not only the information about the relationships, but also the type of rela-
tionships are given which can be used to make better recommender systems than ex-
isting as it will be easy to recommend things to a group of people having similar lik-
4 Datasets and Evaluation Metrics used for Signed Networks
In this section we have provided a list of publicly available real world signed da-
tasets and benchmark datasets used for observational purposes:
website which is a “who-trust-whom” online social network of a general
consumer review site on which users can post reviews about the various products
and services. The rating of reviews is done on the scale of 1 to 5 by different review-
ers who label them by like/dislike based on their trust/distrust on the review.
is a tech-based news website which enables users to tag other users as
“friends” or “foes”. On this site, users can also tag other users negatively. Here, a
friend tag is considered as a positive link and a foe tag is considered as a negative
network is an adminship election dataset in which users cast their votes
to promote individuals for admin post. A positive vote is considered as a positive
link and a negative vote is viewed as a negative link.
Slovene Parliamentary Party Network  represents the relations among 10 po-
litical parties of Slovene Parliamentary. The weights on the links assessed are based
on the scale of -3 to +3, where the positive and negative weight shows similarity and
dissimilarity between the pair of parties respectively.
Gahuku-Gama Subtribes Network  describes the positive and negative alli-
ances among 16 Gahuku-Gama Subtribes. Since, it is an unsigned network, which
can be converted by assuming links between same community as positive and be-
tween different communities as negative.
Table 1. shows the different datasets that are used for analysis of SSNs.
Table 1. Description of the datasets.
Ground Truth Available
Used in articles
4.2 Evaluation metrics for SSNs
Let a signed network be partitioned into communities
and is the adjacency matrix corresponding toie.,
Given a node , and are the positive and the negative degrees of
Modularity  measures how good the partition of the network is, by taking into
account the degree distribution. In signed networks, a division of the network should
be done such that it takes into account the contribution of binary links (positive or
negative links) available among the nodes in the network. Thus, modified definition
of modularity [1, 2],  is given by the equation (2).
when both the nodes and belong to the same community
else and denotes the community to which the node belongs.
For signed overlapping communities, is the number of communities which in-
clude vertex , modularity  is computed as given in the equation (3).
Frustration  measures the unstability in the network. Frustration is the sum of
number of inter-positive links between the communities and the number of intra-
negative links within the [1, 2] communities which is given in the equation (4).
Frustration implies mutually antagonistic or hostile groups with few imbalances.
Therefore, to detect communities frustration minimization can serve as an objective
function [1, 2].
Social Balance Factor: To determine whether a network is structurally balanced or
not, social balance factor ()  can be used. A network with number of balanced
triads and total number of triads given by and respectively, the social
balance factor of the network is computed as follows:
Error Rate: It is based on the concept of frustration, which is used to measure the
partitioning quality of a signed network. The error rate of a partition can be defined
,  as follows:
where, is defined in equation (4). It is obvious that the smaller the value of
the better will be the partition quality.
5 Conclusion and Future Challenges
In this paper, we presented a survey of Signed Social Networks (SSNs) and dis-
cussed trends and perspectives of further research. We have discussed signed network
theories and different metrics used to analyze and evaluate these networks. Signed
networks mimic the real world scenarios, grabbing the attention of many researchers
and thus emerging as a popular research field. There are many research challenges
which are yet to be addressed in this area. Some of them are briefly listed as follows:
It would be interesting to integrate users’ tastes and their trusted friends’ into col-
laborative filtering techniques for more accurate recommendations , .
The role of positive and negative links in online settings can be exploited in the
field of community detection to discover overlapping communities, hierarchical
structures and analysis of time evolving communities which are not yet much ex-
plored in the context of SSNs , , , .
Fusion of trust-distrust and trust-reputation mechanisms into formulation of tech-
niques can enhance the strength and effectiveness of the schemes for SSNs ,
[11, 12], .
Although, a lot of work is done in the field of link prediction, but monolithically
considering links as positive , which is far from the case of real world net-
works as they consist of negative links too. So, development of new procedures to
identify relevant parameters for link prediction using the information obtained
from the SSNs could be a future research direction , , , .
Other promising research direction would be incorporation of trust in recommender
systems and utilization of trust inference mechanism in sparse SSNs to handle the
sparsity problem , .
Discovering new schemes for similarity computation between various profile fea-
tures in SSNs and incorporation of social trust and reputation for quality social
recommendations , .
Information entropy describes the uncertainty associated with a given probability
distribution. The applications of entropy concept in complex networks are widely
and deeply applied. Nevertheless, the application of entropy in signed networks is
currently limited and challenged .
Percolation is one of the best studied processes in statistical physics and serves as a
conceptual framework to treat more factual problems such as collective behavior,
robustness of networks. This concept is still very less dealt in the view of signed
Along with the positive and content-centric interactions, the user generated content
is pervasively available in social media that can be used to investigate, whether us-
er generated content is useful and can be helpful in negative link prediction prob-
Both the theories, social balance and status are applicable only when a link partici-
pates in some triads, which is not always true in the case of real world networks
which are sparse and links may or may not participate in the triads . Hence, the
prediction accuracy will be compromised in these cases. Thus, new psychology so-
cial theories like Emotional Information, Diffusion of Innovations and Individual
Personality could be very helpful for studying the problem of signed link formation
Another interesting research direction is to study link analysis in dynamic signed
networks by deploying the social theories .
Due to the dearth of publicly available datasets with ground truth information it is
difficult to analyze and comprehend the performance of various algorithms on
SSNs for different tasks . Furthermore, the signed directed dataset having inte-
gration of users attributes with links is also not available. Thus, the focus of re-
search community can also be concentrated on development such datasets.
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