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# Are tag clouds useful for navigation? A network-theoretic analysis

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It is a widely held belief among designers of social tagging systems that tag clouds represent a useful tool for navigation. This is evident in, for example, the increasing number of tagging systems offering tag clouds for navigational purposes, which hints towards an implicit assumption that tag clouds support efficient navigation. In this paper, we examine and test this assumption from a network-theoretic perspective, and show that in many cases it does not hold. We first model navigation in tagging systems as a bipartite graph of tags and resources and then simulate the navigation process in such a graph. We use network-theoretic properties to analyse the navigability of three tagging datasets with regard to different user interface restrictions imposed by tag clouds. Our results confirm that tag-resource networks have efficient navigation properties in theory, but they also show that popular user interface decisions (such as "pagination" combined with reverse-chronological listing of resources) significantly impair the potential of tag clouds as a useful tool for navigation. Based on our findings, we identify a number of avenues for further research and the design of novel tag cloud construction algorithms. We also argue that any future algorithm needs to take into account the trade-off between navigational and semantic properties of the generated tag-resource networks. In particular, we introduce a simple method for estimating a so-called semantic penalty induced by a given tag-cloud construction algorithm. Our work is relevant for researchers interested in navigability of emergent hypertext structures, and for engineers seeking to improve the navigability of social tagging systems.
Are Tag Clouds Useful for Navigation?
A Network-Theoretic Analysis
Denis Helic
, Christoph Trattner
, Markus Strohmaier
, Keith Andrews
Knowledge Management Institute
Graz University of Technology
Graz, Austria
Email: {dhelic,markus.strohmaier}@tugraz.at
Institute for Information Systems and Computer Media
Graz University of Technology
Graz, Austria
Email: {ctrattner,kandrews}@iicm.edu
Know-Center, Graz University of Technology, Graz, Austria
Abstract—It is a widely held belief among designers of social
tagging systems that tag clouds represent a useful tool for
navigation. This is evident in, for example, the increasing number
of tagging systems offering tag clouds for navigational purposes,
which hints towards an implicit assumption that tag clouds
support efﬁcient navigation. In this paper, we examine and test
this assumption from a network-theoretic perspective, and show
that in many cases it does not hold. We ﬁrst model navigation
in tagging systems as a bipartite graph of tags and resources
and then simulate the navigation process in such a graph. We
use network-theoretic properties to analyse the navigability of
three tagging datasets with regard to different user interface
restrictions imposed by tag clouds. Our results conﬁrm that tag-
resource networks have efﬁcient navigation properties in theory,
but they also show that popular user interface decisions (such
as “pagination” combined with reverse-chronological listing of
resources) signiﬁcantly impair the potential of tag clouds as a
useful tool for navigation. Based on our ﬁndings, we identify
a number of avenues for further research and the design of
novel tag cloud construction algorithms. We also argue that
any future algorithm needs to take into account the trade-off
between navigational and semantic properties of the generated
tag-resource networks. In particular, we introduce a simple
method for estimating a so-called semantic penalty induced by
a given tag-cloud construction algorithm. Our work is relevant
for researchers interested in navigability of emergent hypertext
structures, and for engineers seeking to improve the navigability
of social tagging systems.
I. INTRODUCTION
In social tagging systems such as Flickr and Delicious, tag
clouds have emerged as an interesting alternative to traditional
forms of navigation and hypertext browsing. The basic idea
is that tag clouds provide navigational clues by aggregating
tags and corresponding resources from multiple sources, and
by displaying them in a visually appealing fashion. Users are
presented with these tag clouds as a means for exploring and
navigating the resource space in social tagging systems.
While tag clouds can potentially serve different purposes,
there seems to be an implicit assumption among engineers of
social tagging systems that tag clouds are speciﬁcally useful to
of tag clouds for interlinking resources in numerous systems
such as Flickr, Delicious, and BibSonomy. However, this
Navigability Assumption has hardly been critically reﬂected
(with some notable exceptions, for example [1]), and has
largely remained untested in the past. In this paper, we will
demonstrate that the prevalent approach to tag cloud-based
navigation in social tagging systems is highly problematic
with regard to network-theoretic measures of navigability. In
a series of experiments, we will show that the Navigability
Assumption only holds in very speciﬁc settings, and for the
most common scenarios, we can assert that it is wrong.
While recent research has studied navigation in social
tagging systems from user interface [2], [3], [4] and network-
theoretic [5] perspectives, the unique focus of this paper is
the intersection of these issues. With that focus, we want to
answer questions such as: How do user interface constraints of
tag clouds affect the navigability of tagging systems? And how
efﬁcient is navigation via tag clouds from a network-theoretic
perspective?
Particularly, we will ﬁrst 1) investigate the intrinsic navi-
gability of tagging datasets without considering user interface
effects, and then 2) take pragmatic user interface constraints
into account. Next, 3) we will demonstrate that for many social
tagging systems, the Navigability Assumption does not hold
and then we will 4) use our ﬁndings to illuminate a path
towards improving the navigability of tag clouds. Thereafter,
we will 5) argue that any new tag-cloud construction algorithm
semantic penalties induced by the network generation process,
and ﬁnally, we will 6) present a simple method for estimating
the semantic penalty.
To the best of our knowledge, this paper is among the ﬁrst to
study what we have called the Navigability Assumption of Tag
Clouds, i. e. the widely held belief that tag clouds are useful
for navigating social tagging systems. One of the main results
of this paper is a more critical stance towards the usefulness of
tag clouds as a navigational aid in tagging systems. We argue
that in order to make use of the full potential of tag clouds,
new ways of thinking about tag cloud algorithms are needed.
The paper is structured as follows: In Section 2 we present
our network-theoretic approach to assessing navigability of
tagging systems. Section 3 describes the analyzed datasets.
Section 4 presents and discusses the analysis results. Based
on our ﬁndings, we call for and discuss new ideas for tag
cloud algorithms in Section 5. In Section 6, we sketch a new
algorithm for constructing tag clouds and present a method for
estimating the semantic properties of the network generated by
that algorithm. Section 7 provides an overview of related work.
Finally, Section 8 concludes the paper and presents directions
for future work.
II. NETWORK-THEORETIC MODEL OF NAVIGATION IN
TAGGING SYSTEMS
A tagging dataset is typically modeled as a tripartite hyper-
graph with V = R U T , where R is the resource set, U is
the user set, and T is the tag set [6], [7], [8]. An annotation
of a particular resource with a particular tag produced by a
particular user is a hyperedge (r, t, u), connecting three nodes
from these three disjoint sets.
Such a tripartite hypergraph can be mapped onto three
bipartite graphs connecting users and resources, users and tags,
and tags and resources. For different purposes it is often more
practical to analyse one or more of these bipartite graphs.
For example, in the context of ontology learning, the bipartite
graph of users and tags has been shown to be an effective
projection [9].
In this paper, we focus on tag-resource bipartite graphs.
These graphs naturally reﬂect the way users are supposed to
adopt tag clouds for navigating social tagging systems. For
example, in many tagging systems, tag clouds are intended to
be used in the following way:
1) The system presents a tag cloud to the user.
2) The user selects a tag from the tag cloud.
3) The system presents a list of resources tagged with the
selected tag.
4) The user selects a resource from the list of resources.
5) The system transfers the user to the selected resource,
and the process potentially starts anew.
We will study this general interaction schema and model
it with a simulated user moving along the edges of the
tag-resource bipartite graph and alternately visiting tag and
resource nodes.
To that end, we introduce a network-theoretic approach for
assessing the navigability and the efﬁciency of navigability in
such a bipartite graph. Ever since Milgram’s small world ex-
periment [10], researchers aimed to understand “navigability”
and in particular “efﬁcient” navigation of networks (for details
see Section VII). Among others, two important results stem
from this line of research: (1) there exist short paths between
people (nodes) in a social network and (2) people are able to
navigate “efﬁciently” through the network having only local
knowledge of the network, i.e. knowing only their personal
contacts.
Kleinberg [11], [12], [13] and also independently Watts
[14] formalised these properties concluding that a navigable
network has a short path between all or almost all nodes in
the network [13]. Formally, such a network has a low diameter
bounded polylogarithmically, i.e. by a polynomial in logN ,
where N is the number of nodes in the network, and there
exists a giant component, i.e. a strongly connected component
containing almost all nodes [13]. Additionally, an “efﬁciently”
navigable network possesses certain structural properties so
that it is possible to design efﬁcient decentralised search
algorithms (algorithms that only have local knowledge of the
network) [11], [12], [13]. The delivery time (the expected
number of steps to reach an arbitrary target node) of such
algorithms is polylogarithmic or at most sub-linear in N.
User navigation in hypertext systems is naturally modeled
as a decentralised search, i.e. at each particular node in the
network, users select a new node having only local knowledge
of the network and following the idea that the selected node
would bring them closest to their destination node. We use
this model to investigate the navigability of tag clouds next.
III. EXPERIMENTAL SETUP
In the following, we conduct experiments aiming to shed
light on the navigability of tag-clouds in social tagging sys-
tems. We are particularly interested in studying how design
decisions, such as what tags to include in a tag cloud or how
many tags to display, effect the navigability of tag clouds.
While, today, designers often base such decisions on intuition
or heuristics, it is our goal to study the consequences of these
decisions experimentally, i.e. by exploring their empirical
effects on the network.
In our experiments, we used three datasets covering a range
of different settings.
Dataset Austria-Forum: This dataset consists of anno-
tations from an Austrian encyclopedia called Austria-
Forum
1
. The dataset contains 32,245 annotations and
12,837 unique resources. The system is at an early phase
of adoption, i.e. not many users currently contribute new
tags.
Dataset BibSonomy: This dataset
2
contains nearly all
916,495 annotations and 235,339 unique resources from a
dump of BibSonomy [15] until 2009-01-01. Annotations
from known spammers have been excluded from the
dataset. This dataset is obtained from a more mature
tagging system.
Dataset CiteULike: This dataset contains 6,328,021 an-
notations and 1,697,365 unique resources and is available
online
3
. Again, this is a dataset acquired from a more
mature tagging system.
Dataset Austria-Forum represents a tagging system at an
early stage of adoption. Datasets BibSonomy and CiteULike
are tagging systems which have reached a certain level of
1
http://www.austria-lexikon.at
2
http://www.kde.cs.uni-kassel.de/ws/dc09/
3
maturity (i.e. attracted a larger set of active users). While
their speciﬁc approaches vary. However, because the datasets
contain complete information about the tripartite graph, we can
experimentally manipulate the data in a way that simulates
different approaches to tag cloud construction consistently
across all datasets. We will describe how we manipulate the
data to simulate different user interface constraints next.
A. User Interface Issues
The ﬁrst user interface restriction which we model is the
size of a tag cloud, i.e. the maximal number of tags displayed
in a tag cloud. While different tagging systems implement
different design choices, we can simulate alternative choices
across all datasets. For example, in some tagging systems the
maximum number of tags in a tag cloud might be 20, while
in others it might be much larger.
Another important issue of tag clouds is the algorithm used
to select the tags to display in a tag cloud. While, in theory,
there are many ways to compute and visualise tag clouds
[16], [17], [3], in practice many tagging systems follow a
simple resource-speciﬁc, TopN algorithm. In resource-speciﬁc
approaches to tag cloud construction, only tags assigned to the
corresponding resources are considered. In TopN approaches,
the top n tags with the highest resource-speciﬁc frequency are
chosen for display in the corresponding tag cloud. In cases
where less than n tags per resource are available, the remaining
slots are left empty.
For the experiments aiming to study the Navigational As-
sumption, we used the TopN algorithm (because it is the
most common) to reconstruct simulated networks of resource-
speciﬁc tag clouds for our three datasets.
Popular tags in a mature tagging system can cover hundreds
or even thousands of resources, which exceeds the pragmatic
limits of a system’s user interface. In this situation, tagging
systems usually resort to limiting the set of resources being
displayed for a given tag (for example, by sorting and “pag-
inating” the list of corresponding resources). To model such
limits, we introduce a pragmatic parameter, the length of the
resource list being presented, and denote it henceforth with k.
In the majority of tagging systems, the resource lists
presented after selecting a tag are usually sorted reverse-
chronologically (the resources most recently tagged are listed
ﬁrst). For simplicity, in our experiments, we select the k
resources for k-limited resource lists randomly.
IV. RESULTS
A. Intrinsic navigability of tagging systems
We start our study by analysing the navigability of tagging
systems in a synthetic network-theoretic case, i.e. without
taking any user interface restrictions into account. The ﬁrst
row in each of Tables I(a), I(b), and I(c) present the obtained
results. The results show the existence of a giant component
connecting almost all of the nodes (98%), as well as the
existence of a low effective diameter (less than 7, i.e. it is
less than polynomial in logN , see Figure 1).
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18
Percentage of pairs of nodes
Number of hops
Austria-Forum EffDiam: 10.7262, G(24171, 64366)
BibSonomy EffDiam: 6.96109, G(291763, 1727992)
CiteULike EffDiam: 6.84779, G(2045200, 12298510)
Austria-Forum
BibSonomy
CiteULike
Fig. 1. Hop plots for three different tagging datasets. We can observe the
shrinking diameter phenomenon [18]: The two mature datasets (Bibsonomy
and CiteULike, the two lines on the left) exhibit a small diameter, while the
Austria-Forum (a tagging system in an early adoption phase, the line on the
right) exhibits a larger diameter, and a larger ratio of long distances between
nodes.
The only exception here is the Austria-Forum dataset. We
speculate that the reason for that is due to the system being
in an early adoption stage. While the effective diameter of
the Austria-Forum dataset is larger than the one in the two
other datasets (see Figure 1), it is still limited polylogarith-
mically, whereas the giant component contains only 77% of
nodes. This result suggests that the Navigability Assumption
depends on the adoption stage of the tagging system under
investigation, i. e. the assumption may only hold for more
mature tagging systems BibSonomy or CiteULike. We leave
the issue of identifying the point in time where immature
tagging systems transition to tagging systems exhibiting more
useful navigational properties to future research. At this point,
we simply observe that the Navigation Assumption is sensitive
to the stage of adoption of a tagging system.
Result 1: The usefulness of tag clouds for navigation is
sensitive to the phase of adoption of the social tagging system.
Figures 2(a), 2(b), and 2(c) show tag (blue), resource
(green), and degree (red) distributions for the analysed
datasets. The tag and resource distributions were obtained
by analysing a unidirectional bipartite graph, i.e. a graph
with only directed links from tags to resources. The out-
degree distribution and the in-degree distribution in this graph
correspond to tag distribution and to resource distribution
respectively. For certain ranges of degrees, both distributions
are power law distributions. There are deviations in the tail of
the tag distribution – these stem from the system tags assigned
to imported resources (see Figures 2(b) and 2(c)). The vertical
line in the tail of Figure 2(c) comes from the existence of
synonym tags in the dataset. The resource distributions exhibit
an exponential cut-off in the tail (see Figure 2(b)), a deviation
in the tail stemming from a test resource (see Figure 2(a)),
10
0
10
1
10
2
10
3
10
4
10
5
10
0
10
1
10
2
10
3
Count (CCDF)
Degree
Austria-Forum G(24171, 64366).
Combined Degree Dist.
Resource Dist.
Tag Dist.
(a) Austria-Forum
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
0
10
1
10
2
10
3
10
4
10
5
Count (CCDF)
Degree
BibSonomy G(291763, 1727992).
Combined Degree Dist.
Resource Dist.
Tag Dist.
(b) BibSonomy
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
0
10
1
10
2
10
3
10
4
10
5
10
6
Count (CCDF)
Degree
CiteULike G(2045200, 12298510).
Combined Degree Dist.
Resource Dist.
Tag Dist.
(c) CiteULike
Fig. 2. Tag, resource, and degree distributions for the three datasets. We can observe that the tag degrees are two or more orders of magnitude greater than
the resource degrees, i.e. the tag distribution strongly dominates the resource distribution for higher degrees. Therefore, the network hubs (high-degree nodes)
are the “head” tags the top tags for TopN tag cloud construction algorithms. It is therefore to expect that limiting of the tag cloud size will not inﬂuence
the navigability of the tag-resource network as the hub nodes are still present in the network.
(a) Austria-Forum
none 0.77 10.73 none sub-lin.
n = 5 0.75 10.99 TopN sub-lin.
n = 10 0.76 11.3 TopN sub-lin.
n = 20 0.76 11.97 TopN sub-lin.
n = 30 0.76 11.05 TopN sub-lin.
k = 5 0.36 12.04 Chron. unnav.
k = 10 0.47 11.16 Chron. unnav.
k = 20 0.56 10.31 Chron. unnav.
k = 30 0.6 10.68 Chron. unnav.
(b) BibSonomy
none 0.98 6.96 none sub-lin.
n = 5 0.94 6.8 TopN sub-lin.
n = 10 0.97 6.87 TopN sub-lin.
n = 20 0.98 6.84 TopN sub-lin.
n = 30 0.98 6.91 TopN sub-lin.
k = 5 0.31 6.82 Chron. unnav.
k = 10 0.4 6.62 Chron. unnav.
k = 20 0.5 6.61 Chron. unnav.
k = 30 0.54 6.65 Chron. unnav.
(c) CiteULike
none 0.98 6.85 none sub-lin.
n = 5 0.93 6.97 TopN sub-lin.
n = 10 0.95 7.07 TopN sub-lin.
n = 20 0.97 7.17 TopN sub-lin.
n = 30 0.97 6.98 TopN sub-lin.
k = 5 0.27 6.89 Chron. unnav.
k = 10 0.36 6.95 Chron. unnav.
k = 20 0.44 6.91 Chron. unnav.
k = 30 0.48 7.05 Chron. unnav.
UIR = UI Restriction, GC = Giant Component, ED = Effective Diameter, UIA = UI Algorithm, NADT = Navigation Algorithm Delivery Time
Chron. = Chronological algorithm, sub-lin. = sub-linear, unnav. = unnavigable network
TABLE I
NAVIGATIONAL PROPERTIES OF THE AUSTRIA-FORUM, BIBSONOMY, AND CITEULIKE TAGGING SYSTEMS.
and a power law distribution as in Figure 2(c).
The degree distribution of the undirected bipartite graph (the
red line in Figures 2(a), 2(b) 2(c)) combines both tag and
resource distributions. For lower degrees, the combined degree
distribution takes the form of the resource distribution, i.e.
the number of resources with low frequencies dominates the
number of tags with low frequencies. For higher degrees, the
combined distribution takes the form of the tag distribution, i.e.
there are more tags with high frequencies than resources with
high frequencies. The tag distribution is two or more orders
of magnitude larger than the resource distribution, i.e. the tag
distribution strongly dominates the resource distribution for
higher degrees. That means that the network hubs (high-degree
nodes) are the “head” tags, i.e. the top tags for TopN tag cloud
construction algorithms.
Due to the existence of a giant component and a low
diameter, tagging systems are intrinsically navigable. In [19],
Adamic shows the existence of efﬁcient decentralised nav-
igation and search algorithms for power law networks. In
principle, a user could ﬁrst navigate to a hub (which is
typically achieved in a few hops in a power law network)
and since hubs have a large out-degree, one can reach the
destination node easily. The delivery time of the algorithm
is sub-linear, although the number of inspected nodes in the
worst-case is O(N ), since sometimes the user needs to inspect
all outgoing links from a hub.
Result 2: Tagging networks are navigable power-law net-
works. For power law networks, efﬁcient sub-linear decen-
B. Tag cloud size
Rows two to ve of Tables I(a), I(b), and I(c) show the
results of applying the TopN algorithm to limit the tag cloud
size on the analysed datasets. From a network-theoretic point
of view, limiting the tag cloud size means limiting the out-
degree of the resource nodes in the bipartite graph. The out-
degree of the resource nodes is two orders of magnitude
smaller then the out-degree of the tag nodes, indicating there
are no resource “hubs” in the network. Therefore, limiting the
tag cloud size does not inﬂuence the network to a large extent.
In other words, the structure of the network is still maintained,
i.e. the network remains a navigable network with navigation
efﬁciency inherent to power law networks.
Result 3: Limiting the tag cloud size to practically feasible
sizes (e.g. 5, 10, or more) does not inﬂuence navigability.
C. Pagination
Rows six to nine of Tables I(a), I(b), and I(c) contain
the results of simulating pagination with resource lists sorted
reverse-chronologically. Even without experiments, it is ev-
ident that limiting the number of links going out from a
tag node has destructive effects on the resulting network.
In other words, limiting the out-degree of hub nodes in a
power-law network destroys the connectivity of the network
as a whole. Our experiments show exactly that: the giant
component collapses, and the largest strongly connected com-
ponent now only contains around 50% or less nodes. As such,
pagination destroys network navigability, and the Navigability
Assumption only holds when we assume that users would be
able and willing to inspect long lists (>10.000) of resources
per tag, which is not reasonable. For example, we know from
search query log research that users rarely click on links
beyond the ﬁrst result page [20]. This yields our ﬁnal result:
Result 4: Limiting the out-degree of high frequency tags
(e.g. through pagination with resource lists sorted reverse-
chronologically) leaves the network vulnerable to fragmenta-
tion. This destroys navigability of prevalent approaches to tag
clouds.
V. IMPLICATIONS
The previous analysis illustrated the vulnerability of tagging
networks to the pagination effect, where a limit is placed on
the number of links going out from paginated tags, i.e. tags
with frequency higher than the pagination parameter k. This
vulnerability is mainly due to the simplicity of the common
pagination algorithm, i.e. the resource list is simply sorted
reverse-chronologically and only the k most recently tagged
resources are presented to the user. The algorithm does not
take into account the current user context, i.e. the resource
where the user clicks on a paginated tag. Rather the same
reverse-chronologically resource list is presented for a given
paginated tag throughout the system.
Let us now investigate possibilities to recover the nav-
igability of tagging networks by means of alternative tag
construction algorithms. To this end, we introduce an adapted
pagination algorithm. A simple generalisation of the pagina-
tion algorithm is to select k different resources out of all
resources tagged with a given paginated tag, depending on the
current user context, i.e. depending on the resource where the
user activates a paginated tag. Let us denote the resources list
of a given paginated tag t with R
t
. In this case, a particular
selection of resources for t becomes a function of a given
resource and parameter k, i.e. L
t
= f (r, k). In other words,
each paginated tag is replaced by as many resource-speciﬁc
tags (t
r
) as there are resources in its resource list. Each
resource-speciﬁc tag is then connected to resources computed
by f (r, k). The pseudo-code of the generalised algorithm is
given in Figure 3.
We now discuss some potential functions f (r, k) for select-
ing resources from the available resource pool and analyse
their inﬂuence on network navigability.
1: Input: G =< V, E >, r, t, k
2: for all r R
t
do
r
to V
r
) to E
5: L
t
f (r, k)
6: for all rr L
t
do
r
, rr) to E
8: end for
9: end for
10: remove t from V
Fig. 3. Generalized pagination algorithm
A ﬁrst obvious choice for f (r, k) is to select k resources
uniformly at random. This approach generates a random graph
as introduced by [21] for each given paginated tag. As [22]
and [23] showed, graphs generated uniformly at random are
typically connected and have with a high probability a
diameter bound by logN (already for out-degrees k 3).
However, since there are no structural clues in a randomly
generated network, a decentralized search algorithm will need
to inspect, in the worst case, all nodes of the network in order
to reach a destination node from the given starting node.
Table II shows the results of a random pagination algorithm
on the three test datasets. All three networks become strongly
connected with a giant component even for low values of k.
As expected, all three networks also possess a low diameter.
B. Hierarchical network model
In [13], Kleinberg introduced the hierarchical network
model and elegantly proved that it is possible to design
efﬁcient decentralised search algorithms for such networks
with a delivery time polynomial in logN (for details see
Section VII). Put simply, Kleinberg showed that, if the nodes
of a network can be organised into a hierarchy, then such
a hierarchy provides a probability distribution for connecting
the nodes in the network. The resulting network is efﬁciently
navigable. A special case of the hierarchical network model is
given when there is a constant number of links leaving a node,
i.e. when the out-degree of a node is limited by a parameter
k as it is the case with pagination. In this case, the tree leaves
contain so-called clusters of nodes, i.e. a collection of a certain
constant number of nodes.
Thus, we developed a hierarchical network generator that 1)
sorts the resource list of a given paginated tag by frequency,
2) creates resource clusters of size 10 by traversing the sorted
resource list sequentially, 3) creates a balanced b-ary (b = 5)
tree where the number of leaves is equal to the number of
the resource clusters, 4) traverses the tree in postorder from
left to right and attaches resource clusters to the tree leaves,
and 5) uses this tree structure to obtain the link probability
distribution for connecting a resource-speciﬁc tag node with
resources of a given paginated tag.
It is important to note that the tree creation process follows
the statistical properties of the tagging dataset only, it has no
(a) Austria-Forum
k=5 0.86 11.7 Random linear
k=10 0.86 11.02 Random linear
k=20 0.85 10 Random linear
k=30 0.84 10.42 Random linear
(b) BibSonomy
k=5 0.99 8.75 Random linear
k=10 0.99 6.97 Random linear
k=20 0.99 6.75 Random linear
k=30 0.99 6.46 Random linear
(c) CiteULike
k=5 0.99 7.98 Random linear
k=10 0.99 7.88 Random linear
k=20 0.99 7.13 Random linear
k=30 0.99 6.86 Random linear
UIR = UI Restriction, GC = Giant Component, ED = Effective Diameter, UIA = UI Algorithm, NADT = Navigation Algorithm Delivery Time
TABLE II
NAVIGATIONAL PROPERTIES OF THE AUSTRIA-FORUM, BIBSONOMY, AND CITEULIKE TAGGING SYSTEMS WITH A RANDOM PAGINATION ALGORITHM.
inherent semantic rationale. As such, it serves primarily as a
statistical tool to improve the efﬁciency of navigability from a
network-theoretic perspective. Table III provides an overview
of the results of the structural network analysis performed with
the three real-life datasets.
Another important observation is that in our model each
paginated tag is a source of a network generated by a hi-
erarchy. These networks are themselves connected through
tag co-occurrence in the dataset, i.e. since tags overlap and
share resources such shared resources link different generated
networks. This makes it more difﬁcult to estimate the delivery
time of a decentralised search algorithm possessing only
the local knowledge. If the algorithm is extended to have
knowledge of all the hierarchies used in the generation of the
networks, then this additional information might be useful in
ﬁnding a destination node faster.
However, more theoretical work is needed to offer a proof
of this intuitive assumption. In addition, it would be interesting
to test these ideas empirically, for example, by implementing
the algorithm and applying it to the real-life datasets. An-
other interesting problem is the ﬁtting of parameters for the
hierarchical network model, for example what is the optimal
combination of the cluster size and the maximum number of
children, with respect to the size of the resource list and the
pagination parameter k.
C. Calculation of resource hierarchies
The hierarchy used in our experiments so far does not pos-
sess any semantic grounding. It is a synthetic hierarchy trying
to optimize navigational aspects of the generated network.
However, improvements of our algorithm will need to take
the semantics of the dataset into account by identifying a
set of resource (metadata) attributes. For example, resource
or even attributes external to the system such as URLs,
full-text, or title. Similar to tag-resource bipartite graphs, a
collection of metadata attributes and resources can be always
represented as yet another bipartite graph. Thus, the discussion
that follows applies for arbitrary resource metadata. However,
for simplicity reasons we refer henceforth only to tag-resource
bipartite graphs.
Let us here shortly discuss possible approaches to obtain
semantically useful resource hierarchies. We can calculate
resource hierarchies by applying e.g. modern hierarchical
clustering algorithms such as K-Means [24] or Afﬁnity Prop-
agation [25] to the tag vectors (see e.g. [26]). Alternatively, if
we deal with text resources it is possible to apply K-Means or
Afﬁnity Propagation on the term vectors. However, in general
case, e.g. in the case when we deal with non-textual resources
such as images or videos we have only tag vectors.
In [27] the authors argue that similarity between tags (the
tag vectors are sparse) are not sufﬁciently great for purely
similarity based hierarchical clustering methods. Therefore,
the authors designed a new algorithm tailored to the speciﬁcs
of the social tagging data. This new algorithm produces so-
called folksonomies
4
– folk-generated taxonomies which are
tag hierarchies. In [28] the authors extend this idea and design
yet another folksonomy creation algorithm.
The input for those folksonomy creation algorithms is the
so-called tag similarity graph – an unweighted graph with tags
as nodes. Two nodes are linked to each other if their similarity
is above a predeﬁned similarity threshold. In the simplest case,
the threshold is deﬁned through tag overlap if the tags do
not overlap in at least one resource than they are not linked
to each other in the tag similarity graph. As the ﬁrst step, the
algorithm calculates node centralities producing a generality
ranking where the most general tags come in the top positions.
Then, the algorithm starts by a single node tree with the most
general tag as the root node and proceeds by iterating through
the generality ranking and adding each tag to the tree the
algorithm calculates the similarities between the current tag
and each tag currently present in the tree and adds the current
tag as a child to its most similar tag.
The algorithm is extensible as it is possible to apply
different similarity and centrality measures, e.g. the algorithm
described in [27] works with the cosine similarity and close-
ness centrality, whereas the algorithm described in [28] works
with the co-occurrence and degree centrality.
The folksonomy algorithms produce tag hierarchies, how-
ever, we are interested in producing resource hierarchies. A
possible approach is to adapt the folksonomy algorithms to
produce global resource hierarchies or resource hierarchies of
a given paginated tag instead of global tag hierarchies. Thus,
the adapted algorithm 1) maps the bipartite tag-resource graph
onto a resource-resource co-occurrence graph, 2) compiles a
generality ranking by calculating a centrality of nodes in the
resource-resource graph, 3) builds the co-occurrence matrix
between resources for similarity calculation, 4) starts with the
4
http://www.vanderwal.net/folksonomy.html
(a) Austria-Forum
k=5 0.85 12.03 Hier. polylog.
k=10 0.86 10.62 Hier. polylog.
k=20 0.85 9.29 Hier. polylog.
k=30 0.84 9.71 Hier. polylog.
(b) BibSonomy
k=5 0.99 8.82 Hier. polylog.
k=10 0.99 7.62 Hier. polylog.
k=20 0.99 6.94 Hier. polylog.
k=30 0.99 6.75 Hier. polylog.
(c) CiteULike
k=5 0.99 8.76 Hier. polylog.
k=10 0.99 7.6 Hier. polylog.
k=20 0.99 6.36 Hier. polylog.
k=30 0.99 5.89 Hier. polylog.
UIR = UI Restriction, GC = Giant Comp., ED = Eff. Diameter, UIA = UI Algorithm, NADT = Navigation Algorithm Delivery Time
Hier. = Hierarchical Algorithm, polylog. = polylogarithmic
TABLE III
NAVIGATIONAL PROPERTIES OF THE AUSTRIA-FORUM, BIBSONOMY, AND CITEULIKE TAGGING SYSTEMS WITH A HIERARCHICAL PAGINATION
ALGORITHM.
most general tag as the root node, 5) iterates through the
generality ranking and attaches the next resource from the
ranking to its most similar resource from the tree. In addition
(to obtain better navigational properties), we can introduce
hierarchy branching factor b and add new resources to the
tree only to those resources that still have available spots for
child resources.
The future work can concentrate on implementation and
evaluation of such algorithms. One problem that the future
work needs to address is scalability resource-resource map-
pings of tagging datasets tend to produce huge networks with
The previous section shows that one way of designing
an efﬁciently navigable network in a tagging system is to
classify the resources of a given paginated tag into a hierarchy.
Thus, to design a navigable network, the pagination algorithm
needs to organise these resource attributes into a hierarchy.
At the same time, it is difﬁcult to expect that an algorithm
taking into account the semantics of resources can produce an
optimal hierarchy that optimizes navigability of the tagging
system as a whole. Rather, the semantic algorithm will tend
to produce an unbalanced tree with a variable cluster size.
As a consequence, the navigational structure generated by
such an algorithm will be sub-optimal, i.e. a decentralised
search algorithm will need to take more steps (investigate
more nodes) to ﬁnd a destination node. We will call this effect
the navigational penalty. Of course, the pagination algorithm
might be altered to produce a tree closer to the optimal tree
from the navigational point of view. This, however, seems
possible only by breaking semantics to a certain extent. We
will call this contrasting effect the semantic penalty. This
reveals an essential trade-off which tag cloud construction
and semantic penalties.
Let us illustrate the navigational and semantic penalties
with an example. Suppose we have 1000 resources about
Austrian cities tagged with Austria”. A particular tagging
system might decide to paginate that tag with a pagination
parameter of k = 20 (listing 20 resources per page). Firstly, the
system would need to semantically classify the resources into
a clustered hierarchy. For example, it could take geography as
the criteria for creating clusters: each cluster corresponding to
an Austrian province. However, the size of the clusters varies
and the province of Vienna (the capital of Austria) might
dominate, since it contains, say, 500 resources. Generating
the network from such an unbalanced hierarchy will result
in a navigational penalty, whereas a new classiﬁcation of the
resources taking into account the Vienna districts as a further
geographical reﬁnement to balance the cluster size may cause
a semantic penalty, if the Vienna province is represented at a
ﬁner level of detail than other provinces.
A. Measuring Semantic Penalty
In the following we present a simple method for estimating
the semantic penalty of different pagination algorithms.
If we ignore pagination and show the complete resource list
R
t
whenever a tag t is selected, t is connected through this
resource list to the set of its co-occurring tags. We represent the
tag co-occurrence of t by means of the co-occurrence vector
c
t
. The dimensions in this vector correspond to tags, and the
value of a particular dimension is the number of resources that
share both t and the dimension tag.
Taking into account pagination, a particular selection of
resources for t is the set L
t
, which is a function of r, k,
and the resource hierarchy in question. We can now introduce
a resource-speciﬁc co-occurrence vector of a given tag t
and denote it as c
r
t
. Again, the vector dimensions are tags,
and the vector values correspond to the number of shared
resources between t and a particular dimension tag. However,
the resources have to belong to L
t
now.
We take the complete co-occurrence vector c
t
of a given
tag t as the ground truth. The resource-speciﬁc co-occurrence
vector c
r
t
of t is than compared against c
t
using cosine
similarity cs (cosine of the angle between vectors c
t
and c
r
t
)
to estimate its alignment with the ground truth:
cs(c
t
, c
r
t
) =
c
t
· c
r
t
kc
t
kkc
r
t
k
(1)
In the next step, we calculate the arithmetic mean of cosine
similarities over all resources of a given paginated tag t:
cs
t
=
1
|R
t
|
X
rR
t
cs(c
t
, c
r
t
) (2)
Then we calculate the arithmetic mean of cs
t
over all tags:
cs =
1
|T |
X
tT
cs
t
(3)
Finally, we obtain a single numerical value the semantic
penalty of a given pagination algorithm as:
sp = 1 cs (4)
We subtract from 1 to express the fact that maximum
similarity would be equivalent to the absence of any semantic
penalty. In addition, we can vary the parameter k to see
how the semantic penalty is distributed with the size of the
paginated page presented to users.
Let us illustrate the intuition behind the semantic penalty
with the following example. In a given tagging dataset, seman-
tics emerge through relations between tags, e.g. the tag Austria
might be related via co-occurrence to tags such as Vienna
(sharing a single resource), Europe (sharing two resources),
and Alps (sharing two resources). Through pagination, some of
the links disappear because resources and their corresponding
tags are omitted from the resource list, e.g. after pagination
Austria is related only to Vienna. Let Austria be the ﬁrst
dimension, Vienna the second, Europe the third, and Alps the
fourth. We have:
c
austria
=
0
1
2
2
c
r
austria
=
0
1
0
0
cs =
1
3
sp =
2
3
Thus, the semantic penalty measures the extent to which the
list of displayed resources is semantically different from the
global semantics of the tag.
Figure 4 compares the semantic penalty of the reverse
chronological, random, and synthetic hierarchical (see Section
V-B) pagination algorithms over all datasets. The preliminary
results show that the semantic penalty does not depend on the
selection of the pagination algorithm but only on the length k
of the paginated list. This result is consistent over all datasets.
Although the results are only preliminary they contain
an interesting observation: While the semantic penalties for
smaller k are still signiﬁcant, as k grows the semantic penalty
decreases very quickly. Even though the algorithms do not
optimize for semantics, paginated lists of length 20 or more do
not induce signiﬁcant semantic penalties. Consistently over all
datasets and all algorithms the semantic penalty for k greater
than 20 drops to 1%. The exception here is again the Austria-
Forum dataset (the semantic penalty is marginal even for small
k): there are only few hub tags in the network and that reduces
the pagination effect on the semantics.
Result 5: Limiting the pagination list length to practically
feasible sizes (e.g. 20, 30, or more) does not introduce a
signiﬁcant semantic penalty.
The further investigation should evaluate semantically op-
timized algorithms to identify potential differences between
the observed and new semantics-aware pagination algorithms.
However, as the semantics is not signiﬁcantly impaired by
pagination (at least for higher values of k), future research
can concentrate on measuring the navigational penalty and
VII. RELATED WORK
We start our review of related work with a brief overview
of network-related research. Research on network navigability
has been inspired by Milgram’s small world experiment [10].
a letter they were then asked to send through their social
networks to a stockbroker in Boston. The striking result of
the study was that, for those letters reaching the destination,
the average number of hops was around 6, i.e. the population
of the USA constituted a “small world”. While the conclusions
have been challenged [29], this experiment has attracted a
great deal of interest in the research community.
Numerous researchers analysed Milgram’s experiment try-
ing to create network models and generators able to produce
such “small world” networks (see for example [30]). The
lattice model by Watts [31] mimics a real-life social network,
where people are primarily connected to their neighbours with
a few “long-range” contacts. The networks generated by this
model have, like the random graph model [22], [23], a giant
component and a diameter bound by logN .
Kleinberg analysed the second result of the Milgram’s
experiment, the ability of people to ﬁnd a short path when
there is such a path between two nodes [11], [12], [13]. He
concluded that there are structural clues in such networks,
which allow people to ﬁnd a short path efﬁciently and argued
that for an “efﬁciently” navigable network there exists a
decentralised search algorithm with delivery time polynomial
in logN .
Kleinberg also designed a number of network models such
as 2D-grid models [12], hierarchical models [13], and group
models [13], and showed that for certain combinations of
parameters, efﬁcient decentralised search algorithms exist.
Particularly, hierarchical network models [13] are based on
the idea that, in many settings, the nodes in a network might
be classiﬁed according to a taxonomy. The taxonomy can be
represented as a b-ary tree and network nodes can be attached
to the leaves of the tree. For each node v, we can create a link
to all other nodes w with the probability that decreases with
h(v, w) where h is the height of the least common ancestor of
v and w in the tree. For a constant out-degree, the nodes are
clustered and then the clusters are attached to the tree. The
link distribution deﬁned by f(h) = (h + 1)
2
b
h
generates a
navigable network with a decentralised search algorithm with
delivery time of O(log
4
b
N).
In related research of tagging systems, tag clouds have
been characterised as a way to translate the emergent vo-
cabulary of a folksonomy into social navigation tools [4],
[32]. Social navigation itself represents a multi-dimensional
concept, covering a range of different issues and ideas. A
distinction between direct and indirect social navigation, for
example, highlights whether navigational clues are provided by
direct communication among users (e.g. via chat), or whether
navigational clues are indirectly inferred from historical traces
left by others [33]. Based on this distinction, our work only
focuses on indirect social navigation in the sense that it studies
0
1
2
3
4
5
5 10 15 20 25 30
Semantic Penalty (Percentage)
Pagination parameter k
Austria-Forum Semantic Penalty
Revers. Chron.
Random
Hierarchical
(a) Austria-Forum
0
1
2
3
4
5
5 10 15 20 25 30
Semantic Penalty (Percentage)
Pagination parameter k
BibSonomy Semantic Penalty
Revers. Chron.
Random
Hierarchical
(b) BibSonomy
0
1
2
3
4
5
5 10 15 20 25 30
Semantic Penalty (Percentage)
Pagination parameter k
CiteULike Semantic Penalty
Revers. Chron.
Random
Hierarchical
(c) CiteULike
Fig. 4. The semantic penalty induced by different pagination algorithms for the three datasets. The two mature datasets (Bibsonomy and CiteULike) exhibit
larger semantic penalties, while the Austria-Forum (a tagging system in an early adoption phase) exhibits signiﬁcantly smaller penalties there are fewer
paginated hub tags in the Austria-Forum and therefore the pagination effect on the semantics is marginal. The semantic penalty does not depend on the
pagination algorithm but solely on the number of resources shown in the paginated list. While semantic penalty for smaller values of k , e.g. 5 and 10 is still
signiﬁcant, limiting the paginated list to a practically feasible length, e.g. 20, does not impair semantics (the semantic penalty drops to 1%).
the effectiveness of traces (“tags”) left by users in tagging
systems. Other types of social navigation emphasise the need
to show the presence of others users, to build trust among
groups of users, or to encourage certain behaviour [33].
Researchers have discussed the advantages and drawbacks
of tag clouds, suggesting that tag clouds are a useful mecha-
nism when users’ search tasks are general and explorative (for
example, learn about Web 2.0), while tag clouds provide little
value for speciﬁc information-seeking tasks (for example, nav-
igate to www.cnn.com) [4]. While the paper at hand focuses on
network-theoretic aspects, cognitive aspects of navigation have
been studied previously using, for example, SNIF-ACT [34]
and social information foraging theory [35]. Other work has
studied the motivations of users for tagging [36], [37], and how
they inﬂuence emergent semantic (as opposed to navigational)
structures. The navigational utility of single tags has been
investigated [38] with somewhat disappointing results. With
time the tags become harder and harder to use as they lose
speciﬁcity and reference too many resources. Such tags are
exactly those paginated tags where new pagination algorithms
are needed.
Navigation models for tagging systems have been also dis-
cussed recently. In [8] authors describe a navigation framework
for tagging systems. The authors apply the framework to
analyze possible attacks on tagging systems. In principle, the
framework identiﬁes a navigation channels as any combination
of the basic elements of a tagging system (users, tags, and
resources). Thus, the speciﬁc combination which we investi-
gated in this paper can be summarized as the resource-tag or
Recent literature also discusses algorithms for the construc-
tion of tag clouds. The ELSABer algorithm [39] represents
an example of such an effort aimed towards identifying
hierarchical relationships between annotations to facilitate
browsing. The work by [40] is another example, introducing
entropy-based algorithms for the construction of interesting
empirical studies of tagging systems have for example focused
on comparing navigational characteristics of tag distributions
to similar distributions produced by library terms [41].
Our work contributes to an increased theoretical understand-
ing about the navigability of current tag cloud algorithms in
social tagging systems. Our experiments identify empirical
problems related to the navigability of tag clouds in three real-
world tagging systems.
VIII. CONCLUSION
The motivation for this research was to examine and test
the widely held belief that tag clouds support efﬁcient nav-
igation in social tagging systems. We have shown that for
certain speciﬁc, but popular, tag cloud scenarios, the so-called
Navigability Assumption does not hold. The results presented
in this paper make a theoretical and an empirical argument
against existing approaches to tag cloud construction. Our
work thereby both conﬁrms and refutes the assumption that
current tag cloud incarnations are a useful tool for navi-
gating social tagging systems. While we conﬁrm that tag-
resource networks have efﬁcient navigational properties in
theory, we show that popular user interface decisions (such as
“pagination” combined with reverse-chronological listing of
resources) signiﬁcantly impair navigability. Our experimental
results demonstrate that popular approaches to using tag clouds
for navigational purposes suffer from signiﬁcant problems.
Building on recent research results from network theory, in
particular hierarchical network models, we have illustrated a
path towards constructing more efﬁciently navigable tag cloud
networks, which are less vulnerable to pagination inﬂuences.
Our ﬁndings suggest that engineers who want to design
effective tag cloud algorithms have to essentially strike a
balance between semantic and navigation penalties, in order to
make navigation in social tagging systems both efﬁcient and
effective. We also presented a simple method for estimating
the semantic penalty. The method is based on measuring
cosine similarity between the non-paginated (ground truth) and
algorithmically generated paginated tag co-occurrence vectors.
The future work needs to investigate the possibilities for
We conclude that in order to make full use of the potential
of tag clouds for navigating social tagging systems, new and
more sophisticated ways of thinking about designing tag cloud
algorithms are needed.
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... There are numerous websites that used tagging even before they were aware of its existence, but it was not until 2001 that the tag clouds began to be used as 19 Helic et al. 37 Other terminologies Usages Rivadeneira 24 ...
... Therefore, the navigation is sensitive to the adoption of the language of tagging-based systems. 37 According to Khusro et al. 4 a tag cloud only is effective when the following conditions are met: ...
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