Structural importance and evolution: an application to financial transaction networks

A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static networks, that do not change over time, but does not consider the dynamics of the network. Here we propose instead to measure the importance of a node based on how much a change to its strength will impact the global structure of the network, which we measure in terms of the spectrum of its adjacency matrix. We apply our method to the identification of important nodes in equity transaction networks, and we show that, while it can still be computed from a static network, our measure is a good predictor of nodes subsequently transacting. This implies that static representations of temporal networks can contain information about their dynamics.