Table 3 Measures of shortest path-related centrality measures commonly used in ecological network analysis.

Betweenness, BC

Quantifies the proportion of shortest paths g between any two nodes i, j, that pass through a focal node v.

\(BC(v)=\frac{\sum _{i\ne v\ne j}{g}_{ij}(v)}{{g}_{ij}}\)

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.

\(SC(v)=\sum _{i\ne v\ne j}{g}_{ij}(v)\)

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.

\(CC(v)=\frac{N-{\rm{1}}}{\sum _{j}{g}_{vj}}\)

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.

\(IIC(v)=\frac{\mathop{\sum }\limits_{i={\rm{1}}}^{n}\mathop{\sum }\limits_{j={\rm{1}}}^{n}{a}_{i}{a}_{j}/({\rm{1}}+n{l}_{ij})}{{A}_{L}^{{\rm{2}}}}\)

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).

\(PC(v)=\frac{\mathop{\sum }\limits_{i={\rm{1}}}^{n}\mathop{\sum }\limits_{j={\rm{1}}}^{n}{a}_{i}{a}_{j}{\dot{p}}_{ij}}{{A}_{L}^{{\rm{2}}}}\)

Landscape networks

⁶²