5,260 research outputs found
Communicability Graph and Community Structures in Complex Networks
We use the concept of the network communicability (Phys. Rev. E 77 (2008)
036111) to define communities in a complex network. The communities are defined
as the cliques of a communicability graph, which has the same set of nodes as
the complex network and links determined by the communicability function. Then,
the problem of finding the network communities is transformed to an all-clique
problem of the communicability graph. We discuss the efficiency of this
algorithm of community detection. In addition, we extend here the concept of
the communicability to account for the strength of the interactions between the
nodes by using the concept of inverse temperature of the network. Finally, we
develop an algorithm to manage the different degrees of overlapping between the
communities in a complex network. We then analyze the USA airport network, for
which we successfully detect two big communities of the eastern airports and of
the western/central airports as well as two bridging central communities. In
striking contrast, a well-known algorithm groups all but two of the continental
airports into one community.Comment: 36 pages, 5 figures, to appear in Applied Mathematics and Computatio
Enhancing community detection using a network weighting strategy
A community within a network is a group of vertices densely connected to each
other but less connected to the vertices outside. The problem of detecting
communities in large networks plays a key role in a wide range of research
areas, e.g. Computer Science, Biology and Sociology. Most of the existing
algorithms to find communities count on the topological features of the network
and often do not scale well on large, real-life instances.
In this article we propose a strategy to enhance existing community detection
algorithms by adding a pre-processing step in which edges are weighted
according to their centrality w.r.t. the network topology. In our approach, the
centrality of an edge reflects its contribute to making arbitrary graph
tranversals, i.e., spreading messages over the network, as short as possible.
Our strategy is able to effectively complements information about network
topology and it can be used as an additional tool to enhance community
detection. The computation of edge centralities is carried out by performing
multiple random walks of bounded length on the network. Our method makes the
computation of edge centralities feasible also on large-scale networks. It has
been tested in conjunction with three state-of-the-art community detection
algorithms, namely the Louvain method, COPRA and OSLOM. Experimental results
show that our method raises the accuracy of existing algorithms both on
synthetic and real-life datasets.Comment: 28 pages, 2 figure
Eigenvector localization as a tool to study small communities in online social networks
We present and discuss a mathematical procedure for identification of small
"communities" or segments within large bipartite networks. The procedure is
based on spectral analysis of the matrix encoding network structure. The
principal tool here is localization of eigenvectors of the matrix, by means of
which the relevant network segments become visible. We exemplified our approach
by analyzing the data related to product reviewing on Amazon.com. We found
several segments, a kind of hybrid communities of densely interlinked reviewers
and products, which we were able to meaningfully interpret in terms of the type
and thematic categorization of reviewed items. The method provides a
complementary approach to other ways of community detection, typically aiming
at identification of large network modules
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