Wang et al.'s CDA returns the propagation-capability score \(PC_i=CD_i+\sum_j(w_{ij}/w_{\max})CD_j\), where \(CD_i=[\alpha d_i+(1-\alpha)s_i]/[1+\exp(-C_i^w)]\). Here d is degree, s is strength, and Cw is Barrat's weighted local clustering coefficient. The maximum edge weight is taken over the whole graph, including other connected components. Inner CD scores remain raw until the final optional normalization of PC.
Arguments
- x
Network input accepted by
centrality.- cda_alpha
Degree-versus-strength mixing weight between zero and one. Default 0.5 follows the source; endpoints select strength and degree respectively while retaining weighted clustering and neighbor contributions.
- ...
Additional arguments to
centrality. Withnormalized = TRUE, positive final scores are divided by their maximum.
Details
Uses finite nonnegative weights on an undirected graph. Zero-weight edges are absent connections. Clustering is set to zero for nodes with fewer than two positive-weight neighbors; this convention agrees with the source's leaf example. Isolates and edgeless graphs score zero. Weights retain their original units: scaling all weights can change scores and rankings because degree and strength are combined. At alpha zero, uniform weight scaling scales scores proportionally; at alpha one, scores are invariant to that scaling. Binary inputs are independent of alpha because their degree and strength coincide.
Self-loops are removed. For weighted directed inputs, opposite arcs
are added into undirected edge weights. Parallel weights are combined
by simplify first, with any remaining parallel edges added.
Without weights, the simple undirected skeleton is used. These are
explicit cograph projections to the source's undirected domain.
mode and shortest-path weight inversion do not affect CDA.
Nonfinite intermediate strengths or scores raise an error, including
when normalization is requested.
References
Wang, Q., Ren, J., Wang, Y., Zhang, B., Cheng, Y., & Zhao, X. (2018). CDA: A Clustering Degree Based Influential Spreader Identification Algorithm in Weighted Complex Network. IEEE Access, 6, 19550-19559, equations 2-6. doi:10.1109/ACCESS.2018.2822844 .
Examples
centrality_cda(igraph::make_ring(5), cda_alpha = 0.5)
#> 1 2 3 4 5
#> 3 3 3 3 3