Comparative definition of community and corresponding identifying algorithm

A comparative definition for community in networks is proposed, and the corresponding detecting algorithm is given. A community is defined as a set of nodes, which satisfies the requirement that each node's degree inside the community should not be smaller than the node's degree toward any other community. In the algorithm, the attractive force of a community to a node is defined as the connections between them. Then employing an attractive-force-based self-organizing process, without any extra parameter, the best communities can be detected. Several artificial and real-world networks, including the Zachary karate club, college football, and large scientific collaboration networks, are analyzed. The algorithm works well in detecting communities, and it also gives a nice description of network division and group formation.