214 research outputs found
Quality functions in community detection
Community structure represents the local organization of complex networks and
the single most important feature to extract functional relationships between
nodes. In the last years, the problem of community detection has been
reformulated in terms of the optimization of a function, the Newman-Girvan
modularity, that is supposed to express the quality of the partitions of a
network into communities. Starting from a recent critical survey on modularity
optimization, pointing out the existence of a resolution limit that poses
severe limits to its applicability, we discuss the general issue of the use of
quality functions in community detection. Our main conclusion is that quality
functions are useful to compare partitions with the same number of modules,
whereas the comparison of partitions with different numbers of modules is not
straightforward and may lead to ambiguities.Comment: 10 pages, 4 figures, invited paper to appear in the Proceedings of
SPIE International Conference "Fluctuations and Noise 2007", Florence, Italy,
20-24 May, 200
Community detection algorithms: a comparative analysis
Uncovering the community structure exhibited by real networks is a crucial
step towards an understanding of complex systems that goes beyond the local
organization of their constituents. Many algorithms have been proposed so far,
but none of them has been subjected to strict tests to evaluate their
performance. Most of the sporadic tests performed so far involved small
networks with known community structure and/or artificial graphs with a
simplified structure, which is very uncommon in real systems. Here we test
several methods against a recently introduced class of benchmark graphs, with
heterogeneous distributions of degree and community size. The methods are also
tested against the benchmark by Girvan and Newman and on random graphs. As a
result of our analysis, three recent algorithms introduced by Rosvall and
Bergstrom, Blondel et al. and Ronhovde and Nussinov, respectively, have an
excellent performance, with the additional advantage of low computational
complexity, which enables one to analyze large systems.Comment: 12 pages, 8 figures. The software to compute the values of our
general normalized mutual information is available at
http://santo.fortunato.googlepages.com/inthepress
Scale-free network growth by ranking
Network growth is currently explained through mechanisms that rely on node
prestige measures, such as degree or fitness. In many real networks those who
create and connect nodes do not know the prestige values of existing nodes, but
only their ranking by prestige. We propose a criterion of network growth that
explicitly relies on the ranking of the nodes according to any prestige
measure, be it topological or not. The resulting network has a scale-free
degree distribution when the probability to link a target node is any power law
function of its rank, even when one has only partial information of node ranks.
Our criterion may explain the frequency and robustness of scale-free degree
distributions in real networks, as illustrated by the special case of the Web
graph.Comment: 4 pages, 2 figures. We extended the model to account for ranking by
arbitrarily distributed fitness. Final version to appear on Physical Review
Letter
Coevolution of Glauber-like Ising dynamics and topology
We study the coevolution of a generalized Glauber dynamics for Ising spins,
with tunable threshold, and of the graph topology where the dynamics takes
place. This simple coevolution dynamics generates a rich phase diagram in the
space of the two parameters of the model, the threshold and the rewiring
probability. The diagram displays phase transitions of different types: spin
ordering, percolation, connectedness. At variance with traditional coevolution
models, in which all spins of each connected component of the graph have equal
value in the stationary state, we find that, for suitable choices of the
parameters, the system may converge to a state in which spins of opposite sign
coexist in the same component, organized in compact clusters of like-signed
spins. Mean field calculations enable one to estimate some features of the
phase diagram.Comment: 5 pages, 3 figures. Final version published in Physical Review
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