Predicting Nodal Influence via Local Iterative Metrics

TL;DR

This paper introduces an iterative metric set derived from local and global topological information to predict nodal influence efficiently, showing that low-order iterative metrics perform nearly as well as complex combined metrics.

Contribution

It proposes a novel iterative metric approach that captures global network information from local data, reducing complexity while maintaining high prediction accuracy.

Findings

Low-order iterative metrics predict influence nearly as well as high-order ones.

The iterative metric set achieves comparable accuracy to combined centrality metrics.

Prediction quality saturates at low iteration orders (~4).

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.