6,351 research outputs found
Two classes of bipartite networks: nested biological and social systems
Bipartite graphs have received some attention in the study of social networks
and of biological mutualistic systems. A generalization of a previous model is
presented, that evolves the topology of the graph in order to optimally account
for a given Contact Preference Rule between the two guilds of the network. As a
result, social and biological graphs are classified as belonging to two clearly
different classes. Projected graphs, linking the agents of only one guild, are
obtained from the original bipartite graph. The corresponding evolution of its
statistical properties is also studied. An example of a biological mutualistic
network is analyzed in great detail, and it is found that the model provides a
very good quantitative fitting of its properties. The model also provides a
proper qualitative description of the statistical features observed in social
webs, suggesting the possible reasons underlying the difference in the
organization of these two kinds of bipartite networks.Comment: 11 pages, 5 figure
Self-organization of collaboration networks
We study collaboration networks in terms of evolving, self-organizing
bipartite graph models. We propose a model of a growing network, which combines
preferential edge attachment with the bipartite structure, generic for
collaboration networks. The model depends exclusively on basic properties of
the network, such as the total number of collaborators and acts of
collaboration, the mean size of collaborations, etc. The simplest model defined
within this framework already allows us to describe many of the main
topological characteristics (degree distribution, clustering coefficient, etc.)
of one-mode projections of several real collaboration networks, without
parameter fitting. We explain the observed dependence of the local clustering
on degree and the degree--degree correlations in terms of the ``aging'' of
collaborators and their physical impossibility to participate in an unlimited
number of collaborations.Comment: 10 pages, 8 figure
Random hypergraphs and their applications
In the last few years we have witnessed the emergence, primarily in on-line
communities, of new types of social networks that require for their
representation more complex graph structures than have been employed in the
past. One example is the folksonomy, a tripartite structure of users,
resources, and tags -- labels collaboratively applied by the users to the
resources in order to impart meaningful structure on an otherwise
undifferentiated database. Here we propose a mathematical model of such
tripartite structures which represents them as random hypergraphs. We show that
it is possible to calculate many properties of this model exactly in the limit
of large network size and we compare the results against observations of a real
folksonomy, that of the on-line photography web site Flickr. We show that in
some cases the model matches the properties of the observed network well, while
in others there are significant differences, which we find to be attributable
to the practice of multiple tagging, i.e., the application by a single user of
many tags to one resource, or one tag to many resources.Comment: 11 pages, 7 figure
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