Local neighbor contribution (Dai et al. 2019) multiplies a node's own contribution \(d_i (1 - 1/d_i)^{d_i - 1}\) by its neighbor contribution, the squared degree times the neighbors' degree sum divided by \(n - 1\). $$LNC_i = d_i^3 \left(1 - \frac{1}{d_i}\right)^{d_i - 1} \frac{\sum_{j \in N(i)} d_j}{n - 1}$$
Arguments
- x
Network input accepted by
centrality.- ...
Further arguments to
centrality, such asnormalized.
Details
The measure is computed on the simple undirected skeleton of the network, so direction, weights, loops and parallel edges are ignored, and it takes no parameters. The count \(n\) is the number of nodes in the whole network, so adding a disconnected component rescales every score and leaves the ranking unchanged. Isolates and the node of a single-node graph score zero. The factorization above is the one that reproduces the source's printed intermediates and Table 1. The Centrality Zoo (section 2.238) replaces the degree by the two-hop neighborhood size and does not reproduce the source's values.
References
Dai, J., Wang, B., Sheng, J., Sun, Z., Khawaja, F. R., Ullah, A., Dejene, D. A. and Duan, G. (2019). Identifying influential nodes in complex networks based on local neighbor contribution. IEEE Access, 7, 131719-131731. doi:10.1109/ACCESS.2019.2939804 .