Separating temporal and topological effects in walk-based network centrality

The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting walks. This article examines the temporal and structural factors influencing these metrics by considering a versatile stochastic temporal network model. We analytically derive formulas to accurately predict the expectation of the broadcast and receive scores when one or more columns in a temporal edge-list are shuffled. These methods are then applied to two publicly available data sets and we quantify how much the centrality of each individual depends on structural or temporal influences. From our analysis, we highlight two practical contributions: a way to control for temporal variation when computing dynamic communicability and the conclusion that the broadcast and receive scores can, under a range of circumstances, be replaced by the row and column sums of the matrix exponential of a weighted adjacency matrix given by the data.