1539-3755
Stochastic fluctuations and the detectability limit of network communities
Floretta
Lucio
Ecole Polytech Fed Lausanne, Lab Biophys Stat, CH-1015 Lausanne, Switzerland
Liechti
Jonas
Ecole Polytech Fed Lausanne, Lab Biophys Stat, CH-1015 Lausanne, Switzerland
Flammini
Alessandro
De Los Rios
Paolo
Ecole Polytech Fed Lausanne, Lab Biophys Stat, CH-1015 Lausanne, Switzerland
2013
We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and every instance of the benchmark, we come to the conclusion that the native, putative partition of the network is completely lost even before the in-degree/out-degree ratio becomes equal to that of a structureless Erdos-Renyi network. We develop a simple iterative scheme, analytically well described by an infinite branching process, to provide an estimate of the true detectability limit. Using various algorithms based on modularity optimization, we show that all of them behave (semiquantitatively) in the same way, with the same functional form of the detectability threshold as a function of the network parameters. Because the same behavior has also been found by further modularity-optimization methods and for methods based on different heuristics implementations, we conclude that indeed a correct definition of the detectability limit must take into account the stochastic fluctuations of the network construction.
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