  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.
