. 2019 Nov 28;9:17826. doi: 10.1038/s41598-019-54206-x

Table 3.

Measures of shortest path-related centrality measures commonly used in ecological network analysis.

Centrality Measure	Definition	Formula	Intended Network type	Reference
Betweenness, BC	Quantifies the proportion of shortest paths g between any two nodes i, j, that pass through a focal node v.	$B C (v) = \frac{\sum_{i \neq v \neq j} g_{i j} (v)}{g_{i j}}$	All types	¹⁵
Stress, SC	Measures the number of shortest paths g between any two nodes i, j, that pass through a focal node v.	$S C (v) = \sum_{i \neq v \neq j} g_{i j} (v)$	All types	¹⁷
Closeness, CC	Measures the average length of the shortest paths from a node v to all the other nodes in the network.	$C C (v) = \frac{N - 1}{\sum_{j} g_{v j}}$	All types	¹⁵
Integral Index of Connectivity, IIC	Measures the degree of connectivity of the entire landscape (of total area A_L) through the calculation of the number of edges in the shortest path nl_ij between patches with area a_i and a_j.	$I I C (v) = \frac{\sum_{i = 1}^{n} \sum_{j = 1}^{n} a_{i} a_{j} / (1 + n l_{i j})}{A_{L}^{2}}$	Binary landscape networks	⁶¹
Probability of Connectivity Index, PC	Quantifies the probability that two species randomly placed across a patchy landscape (of total area A_L) fall into habitat patches a_i and a_j that are reachable from each other with a maximum connectivity probability p_ij, defined as the maximum product probability of all possible paths between patches i and j (including single-step paths).	$P C (v) = \frac{\sum_{i = 1}^{n} \sum_{j = 1}^{n} a_{i} a_{j} {\dot{p}}_{i j}}{A_{L}^{2}}$	Landscape networks	⁶²

Notice that other common centrality measures are based on eigenvectors or dissimilarity scores instead of on the identification of shortest paths and are hence not considered in this work.