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

Predicting Nodal Influence via Local Iterative Metrics