Predicting Nodal Influence via Local Iterative Metrics

Abstract

Nodal spreading influence is the capability of a node to activate the rest of the network when it is the seed of spreading. Combining nodal properties (centrality metrics) derived from local and global topological information respectively is shown to better predict nodal influence than a single metric. In this work, we investigate to what extent local and global topological information around a node contributes to the prediction of nodal influence and whether relatively local information is sufficient for the prediction. We show that by leveraging the iterative process used to derives a classical nodal centrality such as eigenvector centrality, we can define an iterative metric set that progressively incorporates more global information around the node. We propose to predict nodal influence using an iterative metric set that consists of an iterative metric from order $1$ to $K$ that are produced in an iterative process, encoding gradually more global information as $K$ increases. Three iterative metrics are considered, which converge to three classical node centrality metrics respectively. Our results show that for each of the three iterative metrics, the prediction quality is close to optimal when the metric of relatively low orders ($K\sim4$) are included and increases only marginally when further increasing $K$. The best performing iterative metric set shows comparable prediction quality to the benchmark that combines seven centrality metrics, in both real-world networks and synthetic networks with community structures. Our findings are further explained via the correlation between an iterative metric and nodal influence, the convergence of iterative metrics and network properties.