Centrality for graphs with numerical attributes

Identification of important actors in social networks is a hard task but with various interesting applications such as in information recommendation or for viral marketing. Existing centrality measures evaluate the importance of an actor in considering only the structural positions regardless of prior information on these actors such as their popularity, accessibility or behavior. A few measures have been proposed for weighted networks, notably the three common measures of centrality: degree, closeness, and betweenness. However, these extended versions have solely focused on the weights of ties and not on the attributes of nodes. This article proposes generalizations that combine these both aspects. We present a set of measures, based on conventional centrality indicators, suited to weighted attributed graphs where the nodes are characterized by attributes. We illustrate the benefits of this approach on real attributed graphs. Experiments have validated the contribution of the links weights and attributes, especially for the detection of information broadcasters in social networks.