Communities in networks - a continuous approach

A system of differential equations is proposed designed as to identify communities in weighted networks. The input is a symmetric connectivity matrix $A_{ij}$. A priori information on the number of communities is not needed. To verify the dynamics, we prepared sets of separate, fully connected clusters. In this case, the matrix $A$ has a block structure of zeros and units. A noise is introduced as positive random numbers added to zeros and subtracted from units. The task of the dynamics is to reproduce the initial block structure. In this test, the system outperforms the modularity algorithm, if the number of clusters is larger than four.