A new method for detecting communities and their centers using the Adamic/Adar Index and game theory

The importance of graphs as a tool for modeling phenomena has increased the interest of researchers to study related concepts. Community detection, as an important analyze on the graphs, has attracted researchers from various fields such as sociology, biology, physics and interdisciplinary sciences in recent years. Unlike most of the existing methods that only focus on the detection of communities, the proposed method of this research considers finding community centers too. In the present paper, we rely on the idea that community members are able to create new edges between each other. Later, we show that this idea does not contradict with dense connections inside each community. Using new definitions, we propose a new way to define both community centers and communities itself. Taking this idea, we will detect local primary nodes using the Adamic/Adar (AA) index and expand the communities around these nodes in a game theory based framework. Experimental results obtained by testing the proposed method on real-world and synthetic datasets show the effectiveness of the proposed method.