Unfolding Ego-Centered Community Structures with "A Similarity Approach"

We propose a framework to unfold the ego-centered community structure of a given node in a network. The framework is not based on the optimization of a quality function, but on the study of the irregularity of the decrease of a similarity measure. It is a practical use of the notion of multi-ego-centered community and we validate the pertinence of the approach on a real-world network of wikipedia pages. 1 Context and related work Many real-world complex systems, such as social or computer networks can be modeled as large graphs, called complex networks. Because of the increasing volume of data and the need to understand such huge systems, complex networks have been extensively studied these last ten years. Due to its applications, notably in market research and classification, and its intriguing nature, the notion of communities of nodes and their detection has been at the center of this research. For an extensive survey on community detection, we refer to [FOR10]. Communities are clearly overlapping in real world systems, especially in social networks, where every individual belongs to various communities: family, colleagues, groups of friends, etc. Finding all these overlapping communities in a huge graph is very complex: in a graph of n nodes there are 2 such possible communities and 2 n such possible community structures. Even if these communities could be efficiently computed, it may lead to uninterpretable results. However, some studies have still tackled this problem, such as [PAL05] and [EVA09]. Because of the complexity of overlapping communities detection, most studies have restricted the community structure to a partition, where each node belongs to one and only one community. This problem, also very complex, does not have a perfect solution for now, however several algorithms with very satisfying results exist, in particular the Louvain method [BLO08] which optimizes the modularity [GIR02] in an agglomerative fashion, and Infomap [ROS08]. Another approach, to keep the realism of overlapping communities, but without making the problem too complex, is to focus on a single node and try to find all the communities it belongs to, which we call ego-centered communities. This has been extensively studied following a quality function approach: starting from a group where only the given node is included and optimizing step by 3 Groups of nodes very connected to one-another, but loosely connected to the outside.