17,000 research outputs found
Computing communities in large networks using random walks
Dense subgraphs of sparse graphs (communities), which appear in most
real-world complex networks, play an important role in many contexts. Computing
them however is generally expensive. We propose here a measure of similarities
between vertices based on random walks which has several important advantages:
it captures well the community structure in a network, it can be computed
efficiently, it works at various scales, and it can be used in an agglomerative
algorithm to compute efficiently the community structure of a network. We
propose such an algorithm which runs in time O(mn^2) and space O(n^2) in the
worst case, and in time O(n^2log n) and space O(n^2) in most real-world cases
(n and m are respectively the number of vertices and edges in the input graph).
Experimental evaluation shows that our algorithm surpasses previously proposed
ones concerning the quality of the obtained community structures and that it
stands among the best ones concerning the running time. This is very promising
because our algorithm can be improved in several ways, which we sketch at the
end of the paper.Comment: 15 pages, 4 figure
Two betweenness centrality measures based on Randomized Shortest Paths
This paper introduces two new closely related betweenness centrality measures
based on the Randomized Shortest Paths (RSP) framework, which fill a gap
between traditional network centrality measures based on shortest paths and
more recent methods considering random walks or current flows. The framework
defines Boltzmann probability distributions over paths of the network which
focus on the shortest paths, but also take into account longer paths depending
on an inverse temperature parameter. RSP's have previously proven to be useful
in defining distance measures on networks. In this work we study their utility
in quantifying the importance of the nodes of a network. The proposed RSP
betweenness centralities combine, in an optimal way, the ideas of using the
shortest and purely random paths for analysing the roles of network nodes,
avoiding issues involving these two paradigms. We present the derivations of
these measures and how they can be computed in an efficient way. In addition,
we show with real world examples the potential of the RSP betweenness
centralities in identifying interesting nodes of a network that more
traditional methods might fail to notice.Comment: Minor updates; published in Scientific Report
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