Research On Community Detection In Networks Via Consensus Dynamics

The recent years has witnessed a great deal of interest in the science of complex networks.This is partially due to the growing interest in understanding intriguing complex systems in nature and the real world,and also due to its broad applications in many areas as diverse as the internet,neural networks,social networks and biological organizations.With the deepening of the study on complex networks,researchers found that the distribution of nodes in networks is not characterized by random,but organized by some certain rules.It is with great importance to reveal and understand these rules.One of the most distinctive properties existed in many complex networks is “community structure”.Identifying these communities is fundamentally important to reveal the deep structure of the entire network and functional patterns that may be causal in forming such a structure,thus reducing the difficulty and complexity of the research.However,only study the topology of the network and analyze its inherent characteristics cannot embody its evolution rules.Then an important object of study on complex networks is to understand how the topological structure influences on the dynamical process.Therefore,this paper investigates community structure in networks by dynamic method.Unlike the traditional dynamic methods such as spin model,random walk and synchronization,we detect the communities in networks by consensus dynamics.This paper firstly solves the community detection problem by analyzing the influences that the community structure exerted on the consensus process.We analyze the dynamical process towards consensus and show that those sets of densely interconnected nodes corresponding to well-defined communities appear in different time scales.Thus,it is available to identify the community structure of a graph according to the route of an agreement problem solved.Then we propose two approaches to extract information about how nodes reach an agreement in a sequential process by visualizing different measured quantities.Next,this paper detect communities in networks via consensus dynamics and space transform.Firstly the consensus process of a network is emulated to a diffusion process in a finite space.Then assign an initial pressure to one node and the corresponding pressure distribution vectors are used to describe the influence that each node exerts on the network.After that the K-Nearest Neighbor is used to translate the community detection problem to a cluster analysis problem in Euclidean n-spaces could cluster groups of nodes.At last we can recognize the best partition by drawing clustering tree and modularity distribution.Except for exploring community structure in networks by consensus dynamics,this paper also seek group consensus in networks of dynamic agents under directed topology.The sufficient conditions which group consensus can reach under the given protocol are obtained and the consensus process could be controlled because of the newly added feedback controllers in our protocol.Then the dynamic performance of our protocol is discussed and several criteria are presented to infer the consensus space of different groups.At last we summarize the whole paper and imply some problems needed to research and explore in the future.