The centrality of edges based on their role in induced triads

The prevalence of induced triads play an important role in characterising complex networks, supporting approaches for assessment of dynamic and partially obfuscated scenarios. In this paper we introduce a new local edge-centrality measure that is designed to be deployed in this context for complex networks and is highly scalable. It signifies the importance an edge plays within induced triads for a directed network. We observe that an edge can play one of two roles in providing connectivity within any particular triad, based on whether the edge supports connectivity to the third node or not. We call these alternative states overt and covert. As an edge may play alternative roles in different induced triads, this allows us to assess the local importance of an edge across multiple induced substructures. We introduce theory to count the number of induced triads in which an edge is overt and covert. Using 34 data sets derived from public sources, we show how the presence of overt and covert edges can be used to profile diverse real-world networks. The relationship with global network analysis metrics is examined. We observe that overt and covert edge centrality is useful in further differentiating classes of network, when considered in combination with conventional global network analysis metrics.