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Differential equations as a tool for community identification.

We consider the task of identification of a cluster structure in random networks. The results of two methods are presented: (i) the Newman algorithm [M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004)]; and (ii) our method based on differential equations. A series of computer experiments is performed to check if in applying these methods we are able to determine the structure of the network. The trial networks consist initially of well-defined clusters and are disturbed by introducing noise into their connectivity matrices. Further, we show that an improvement of the previous version of our method is possible by an appropriate choice of the threshold parameter beta . With this change, the results obtained by the two methods above are similar, and our method works better, for all the computer experiments we have done.