Spreading strength is a topological measure that quantifies a node's influence in spreading processes, taking into account its indirect propagation through the neighborhood [2]. The spreading strength \(c_{ss}(i)\) of node \(i\) is defined as
\[
c_{ss}(i) = \sum_{j \in \mathcal{N}(i)} \left( 1 + d_j^{out} \left( 1 + \frac{|D_{ij,2}|}{4} \right)^{α} \right),
\]
where \(\mathcal{N}(i)\) is the set of neighbors of node \(i\), \(d_j^{out} = |\{ l \in \mathcal{N}(j) : l \notin \mathcal{N}(i) \cup \{i\} \}|\) is the number of neighbors of \(j\) outside \(i\)'s neighborhood, \(|D_{ij,2}|\) is the number of paths of length 2 connecting \(i\) and \(j\), and \(α\) is a tunable parameter (e.g., \(α = 0.5\)). This formulation captures both the local connectivity of neighbors and the potential for spreading beyond the immediate neighborhood.

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Yu, Z., Shao, J., Yang, Q., & Sun, Z. (2019). Profitleader: Identifying leaders in networks with profit capacity. World Wide Web, 22(2), 533-553. doi: 10.1007/s11280-018-0537-6.