. 2019 Jul 23;9:10692. doi: 10.1038/s41598-019-47119-2

Table 2.

List of the complex network functioning measures used in this research.

Measure	Formula	Functioning meaning	Ref.
LCC	$L C C = \max (S_{j})$ S_j: size of the j cluster	The LCC is the largest number of nodes connected by at least one path in the network and can be viewed as a binary (unweighted) measure of the network functioning.	^1– 3
Eff	$E f f = \frac{1}{N \cdot (N - 1)} \sum_{i \neq j \in G} \frac{1}{d (i, j)}$ N: number of nodes D_i,j: length of the weighted shortest path between node i and j	The efficiency (Eff) is a measure of the global complex network capacity to deliver information among system constituents (nodes) and allows a precise quantitative evaluation of the weighted networks functioning. It is computed considering the link weights.	^13, 14, 22
Effbin	$E f f b i n = \frac{1}{N \cdot (N - 1)} \sum_{i \neq j \in G} \frac{1}{d (i, j)}$ N: number of nodes D_i,j: length of the binary shortest path between node i and j	The efficiency (Eff_bin) is a measure of the global complex network capacity to deliver information among system constituents (nodes). It is computed over the binary network, where all link weights equals 1.	^13, 14, 22
TF	$T F = \sum_{i = 1}^{N} \sum_{j = 1}^{N} w_{i, j}$	The total flow in the system (TF) is the sum of the link weights; it represents the simplest weighted measure evaluating the actual or the potential flows between couple of nodes in the networks.	¹⁷