centrality_heatmap: Heatmap, Flow Coefficient, Local Entropy, Weighted h-index,...

In cograph: Analysis and Visualization of Complex Networks

Heatmap, Flow Coefficient, Local Entropy, Weighted h-index, Redundancy

Description

Five local measures.

Usage

centrality_heatmap(x, mode = "all", ...)

centrality_flow_coefficient(x, ...)

centrality_local_entropy(x, mode = "all", ...)

centrality_weighted_h_index(x, mode = "all", ...)

centrality_redundancy(x, ...)

Arguments

x	Network input (matrix, igraph, network, cograph_network, tna object).
mode	For directed networks: "all" (default), "out" (distances along out-edges), or "in".
...	Additional arguments passed to centrality.

Details

heatmap (Duron 2020)

Farness minus the mean farness of the neighbors, C(v) = f(v) - \frac{1}{k_v} \sum_{u \in N(v)} f(u), with f the sum of hop distances to reachable nodes. Lower is more central. Isolates score NaN. Reproduces Table 1 of the paper.

flow_coefficient (Honey et al. 2007)

Among ordered pairs of distinct neighbors, the fraction joined by a two-step path through the node but not by a direct link, as implemented in the Brain Connectivity Toolbox. On an undirected graph it equals one minus the clustering coefficient; it carries new information only on directed graphs. Nodes with fewer than two neighbors score 0.

local_entropy (Nie et al. 2016)

-\sum_{j \in N(i)} k_j \ln k_j, as printed by the sources. Always non-positive and more negative for larger, denser neighborhoods, so lower is more central; isolates score 0, the maximum. The original article is closed access; the formula is that of the Zoo and of Omar and Plapper's 2021 survey, which agree.

weighted_h_index (Gao et al. 2019)

h-index of the multiset in which each neighbor j contributes the topological weight k_i k_j repeated k_j times. Edge weights on the input play no role.

redundancy (Burt 1992; Borgatti 1997)

Mean degree of the node's neighbors within its ego network, 2 t_i / k_i; equal to degree minus effective size. Higher = fewer structural holes. Reproduces Borgatti's worked example.

heatmap, local_entropy and weighted_h_index follow mode; the others ignore direction. Edge weights are ignored.

Value

Named numeric vector, one value per node.

References

Duron, C. (2020). Heatmap centrality: A new measure to identify super- spreader nodes in scale-free networks. PLOS ONE, 15(7), e0235690.

Honey, C. J., Kotter, R., Breakspear, M., & Sporns, O. (2007). Network structure of cerebral cortex shapes functional connectivity on multiple time scales. PNAS, 104(24), 10240-10245.

Nie, T., Guo, Z., Zhao, K., & Lu, Z.-M. (2016). Using mapping entropy to identify node centrality in complex networks. Physica A, 453, 290-297.

Gao, L., Yu, S., Li, M., Shen, Z., & Gao, Z. (2019). Weighted h-index for identifying influential spreaders. Symmetry, 11(10), 1263.

Borgatti, S. P. (1997). Structural holes: Unpacking Burt's redundancy measures. Connections, 20(1), 35-38.

See Also

centrality_effective_size, centrality_transitivity.

Examples

star5 <- matrix(0, 5, 5)
star5[1, 2:5] <- 1; star5[2:5, 1] <- 1
rownames(star5) <- colnames(star5) <- LETTERS[1:5]
centrality_heatmap(star5)
centrality_weighted_h_index(star5)
centrality_redundancy(star5)

cograph documentation built on Sept. 30, 2026, 5:08 p.m.