Assessing vertex relevance based on community detection

The community structure of a network conveys information about the network as a whole, but it can also provide insightful information about the individual vertices. Identifying the most relevant vertices in a network can prove to be useful, especially in large networks. In this paper, we explore different alternatives for assessing the relevance of a vertex based on the community structure of the network. We distinguish between two relevant vertex properties - commitment and importance - and propose a new measure for quantifying commitment, Relative Commitment. We also propose a strategy for estimating the importance of a vertex, based on observing the disruption caused by removing it from the network. Ultimately, we propose a vertex classification strategy based on commitment and importance, and discuss the aspects covered by each of the two properties in capturing the relevance of a vertex.