Overlapping community detection via network dynamics

Abstract

The modular structure of a network is closely related to the dynamics toward clustering. In this paper, a method for community detection is proposed via the clustering dynamics of a network. The initial phases of the nodes in the network are given randomly, and then they evolve according to a set of dedicatedly designed differential equations. The phases of the nodes are naturally separated into several clusters after a period of evolution, and each cluster corresponds to a community in the network. For the networks with overlapping communities, the phases of the overlapping nodes will evolve to the interspace of the two communities. The proposed method is illustrated with applications to both synthetically generated and real-world complex networks.

The Kuramoto model in complex networks

“…The limitation of assigning natural frequencies according to a pre-defined modular structure was overcome in a modified approach [169,170]. Specifically, the following model was considereḋ…”

“…With the introduction of positive and negative couplings, the phases of connected nodes will attract each other, whereas unconnected nodes will be repelled. Thus, as shown in [169,170], the longtime behavior of phases θ i (t) will quantify the membership of each node, and those one lying with intermediate values are identified as belonging to interfaces between two or more communities. Furthermore, in contrast to [166,167] the accuracy of the generalized method no longer depends on the scale of the coupling strength, since the emergence of phase lag between nodes belonging to different communities is guaranteed by the presence of negative couplings [169,170].…”

“…Thus, as shown in [169,170], the longtime behavior of phases θ i (t) will quantify the membership of each node, and those one lying with intermediate values are identified as belonging to interfaces between two or more communities. Furthermore, in contrast to [166,167] the accuracy of the generalized method no longer depends on the scale of the coupling strength, since the emergence of phase lag between nodes belonging to different communities is guaranteed by the presence of negative couplings [169,170]. It is worth mentioning that many papers analytically investigated the lowdimensional behavior of Kuramoto oscillators coupled in fully connected graphs but organized into subpopulations characterized by different frequency and couplings distributions [171][172][173][174][175][176][177].…”

Clustering dynamics of complex discrete-time networks and its application in community detection

“…But with the original algorithm stated in Ref. 37, which uses only phases information for community detection, a network with many (more than three usually) communities is not applicable because the stable phases of two or more communities may be mixed together. The methods either by phase synchronization or phase clustering in previous works use an oscillator model governed by differential equation.…”

“…In Ref. 37, it is recommended to use stable clustering phenomenon for community detection. The stable phases of the nodes in the same community are almost synchronized, whereas the states of the nodes in different communities are far from synchronization.…”