cograph (version 2.7.2)

centrality_community_based: Community-Based Centrality, Comm Centrality and Community-Based Mediator

Description

Three community-aware measures that need a partition (membership).

Usage

centrality_community_based(x, membership = NULL, mode = "all", ...)
centrality_comm_centrality(
  x,
  membership = NULL,
  mode = "all",
  comm_r = "max_intra",
  ...
)
centrality_community_mediator(x, membership = NULL, mode = "all", ...)

Value

Named numeric vector, one value per node.

Arguments

x

Network input (matrix, igraph, network, cograph_network, tna object).

membership

Community labels, one per node. Required; without it the function warns and returns NA.

mode

For directed networks: "all" (default), "out", or "in".

...

Additional arguments passed to centrality.

comm_r

Scale \(R\) of Comm centrality: "max_intra" (default) or a single positive number. Anything else raises a cograph_bad_parameter error.

Conditions

Raises an error of class cograph_bad_membership when membership is not one non-missing label per node.

Details

community_based (Zhao, Wang, Zhang & Zhu 2015)

\(CbC(i) = \sum_w d_{iw} S_w / N\): every link of \(i\) counts the size \(S_w\) of the community it lands in. No parameters. Reproduces Table 1 of the paper and Table 1 of Tulu et al. (2018).

comm_centrality (Gupta, Singh & Cherifi 2016)

$$CC(i) = (1 + \mu_C)\, \frac{k^{in}_i}{\max_{j \in C} k^{in}_j} R + (1 - \mu_C) \left(\frac{k^{out}_i}{\max_{j \in C} k^{out}_j} R\right)^2,$$ where \(k^{in}, k^{out}\) are the intra- and inter-community degrees, \(\mu_C\) the mean inter-link fraction in \(i\)'s community, and \(R\) a scale. The default comm_r = "max_intra" is the paper's recommended \(R = \max_{j \in C} k^{in}_j\) per community; a number applies one global \(R\). The equation uses \(1 + \mu_C\) although the paper's prose says \(\mu_C\); the equation is implemented. A community without intra (inter) links contributes 0 through that term.

community_mediator (Tulu, Hou & Younas 2018)

\(CbM(i) = H_i \, d_i / \sum_j d_j\), with \(H_i\) the base-2 Shannon entropy of \(i\)'s link distribution over the communities. Nodes linked to one community only score 0. Base 2 is what reproduces the paper's Table 1.

Higher = more central in all three. Under mode = "out" or "in" only out- or in-links count; edge weights are ignored.

References

Zhao, Z., Wang, X., Zhang, W., & Zhu, Z. (2015). A community-based approach to identifying influential spreaders. Entropy, 17(4), 2228-2252.

Gupta, N., Singh, A., & Cherifi, H. (2016). Centrality measures for networks with community structure. Physica A, 452, 46-59.

Tulu, M. M., Hou, R., & Younas, T. (2018). Identifying influential nodes based on community structure to speed up the dissemination of information in complex network. IEEE Access, 6, 7390-7401.

See Also

centrality_community_hub_bridge, centrality_participation.

Examples

adj <- matrix(0, 6, 6)
adj[cbind(c(1, 1, 2, 4, 4, 5, 3), c(2, 3, 3, 5, 6, 6, 4))] <- 1
adj <- adj + t(adj)
rownames(adj) <- colnames(adj) <- LETTERS[1:6]
centrality_community_based(adj, membership = c(1, 1, 1, 2, 2, 2))
centrality_comm_centrality(adj, membership = c(1, 1, 1, 2, 2, 2))
centrality_community_mediator(adj, membership = c(1, 1, 1, 2, 2, 2))