Ranking the Importance Level of Intermediaries to a Criminal using a Reliance Measure

Current research into discovering important intermediate nodes in a network suspected of containing criminal activity, is highly dependent on network centrality values. Betweenness centrality, for example, is widely used to rank the nodes that act as brokers in the shortest paths connecting all source with all end nodes in a network. However both the shortest path node betweenness as well as the linearly scaled betweenness can only show rankings for all the nodes in a network, and not for just a subset of source nodes. In this paper we explore the mathematical concept of pair-dependency of a source on intermediate nodes, adapting the concept to criminal relationships and introducing a new source-intermediate reliance measure. To illustrate our measure, we apply it to rank the nodes in the Enron email dataset and the Noordin Top Terrorist networks. We compare the reliance ranking with Google PageRank, Markov centrality as well as betweenness centrality and show that a criminal investigation using the reliance measure, will lead to a different prioritisation in terms of possible people to investigate. While the ranking for the Noordin Top terrorist network yields more extreme differences than the Enron email transaction network, in the latter the reliance values for the set of finance managers immediately identified another employee convicted of money laundering.