The (not so) critical nodes of criminal networks

One of the most basic question in the analysis of social networks is to find nodes that are of particular relevance in the network. The answer that emerged in the recent literature is that the importance, or centrality, of a node x is proportional to the number of nodes that get disconnected from the network when node x is removed. We show that while in social networks such important nodes lie in their cores (i.e., maximal subgraphs in which all nodes have degree higher than a certain value), this is not necessarily the case in criminal networks. This shows that nodes whose removal affects large portions of the criminal network prefer to operate from network peripheries, thus confirming the intuition of Baker and Faulkner [4]. Our results also highlight structural differences between criminal networks and other social networks, suggesting that classical definitions of importance (or centrality) in a network fail to capture the concept of key players in criminal networks.