The improved Iterative Resource Allocation (IIRA) method is an extension of the iterative resource allocation (IRA) method that incorporates both neighbor centrality and the spreading rate to evaluate node influence [2]. In IIRA, each node \(i\) is initially assigned a resource \(I_i(0)\), which is iteratively distributed to its neighbors according to their centrality and the spreading rate \(β\). After a sufficient number of iterations \(t\), the resource \(I_i(t)\) of each node approaches a steady state, and the final resource values are used to identify influential nodes.
The diffusion process can be formalized using the \(N \times N\) stochastic matrix \(P\), with entries
\[
p_{ij} = \left( 1 - (1-β)^{d_i} \right) \frac{a_{ij} c_i}{\sum_{k=1}^N a_{ik} c_k},
\]
where \(a_{ij}\) is the adjacency matrix, \(c_i\) represents a chosen centrality of node \(i\), and \(d_i\) is its degree. Zhong et al. [2] set the spreading rate \(β = 0.2\) and the number of iterations \(t = 50\), demonstrating that IIRA computed using closeness centrality provides more accurate identification of influential nodes than the version based on eigenvector centrality.

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] Zhong, L. F., Liu, J. G., & Shang, M. S. (2015). Iterative resource allocation based on propagation feature of node for identifying the influential nodes. Physics Letters A, 379(38), 2272-2276. doi: 10.1016/j.physleta.2015.05.021.