Centrality measures identifying dominant promoters and inhibitors in signed networks

Identifying the global regulatory importance of nodes in a regulatory network is important in many biological and competitive social networks, but the majority of measures of social networks are not easily adaptable to signed networks. In this talk, I use the concept of `social balance' to identify important regulators in signed networks, which can be understood as `the inhibitor of my inhibitor is my promotor' in signed networks. This approach is used to define two related measures of centrality incorporating the topology and signs of the links in a manner similar to Katz and betweenness centrality. To illustrate the utility of this approach in identifying important nodes in a signed network, I generate an ensemble of hierarchical majority-rule networks divided into top regulators, middle men (both both regulators and regulated), and workhorses (only regulated). I show that signed Katz centrality is able to identify the net effect of node removal, where nodes with large positive centrality are overall downstream promoters, nodes with very negative centrality are overall downstream inhibitors, and nodes with near-zero centrality have mixed effects. This measure of network centrality provides a new method for understanding complex signed networks in a variety of contexts.