Table 1.

Network descriptors used in this study.

Symbol	Interpretation	Mathematical expression	Implication
G	Graph	–	Weighted and undirected graph
V	Set of vertices	–	Set of n-nodes
E	Set of edges	–	Set of n*(n−1)/2 maximum edges
Nleaf	Leaf nodes	–	Number of nodes with degree equal to one
wij	Weight	–	Weight of the edge connecting nodes i and j
$t_i^w$	Number of triangles	$t_i^w=\frac{1}{2}{{\displaystyle \sum _{j,k\in V}\left(w_{ij}{w}_{jk}{w}_{kl}\right)}}^{1/3}$	Weighted geometric mean of triangles around a node
$d_{ij}^w$	Shortest path	-	Shortest weighted path between nodes i and j
$C_i^w$	Weighted clustering coefficient	$C_i^w={\displaystyle \sum _{i\in G}\frac{2t_i^w}{k_i(k_i-1)}}$	Segregation measure that quantifies the local connectedness of a network
Cw	Average weighted clustering coefficient	$C^w=\frac{1}{n}{\displaystyle \sum _{i\in G}{C}_i^w}$	A global version of the weighted clustering coefficient used for computing σw
Lw	Weighted characteristic path length	$L^w=\frac{1}{n}{\displaystyle \sum _{i\in G,j\ne i}\frac{d_{ij}^w}{n-1}}$	Integration measure
γw	Gamma	${\gamma }^w=C^w/{C^w}_{rand}$	Ratio of the weighted clustering coefficients between original and random networks
λw	Lambda	${\lambda }^w=L^w/{L^w}_{rand}$	Ratio of weighted path lengths between original and random networks
σw	Small-worldness index	σw = γw/λw	Reveals whether a network has an optimal organization or not
conn	Connectivity	$conn=\frac{1}{n(n-1)}·{\displaystyle \sum _{\begin{array}{c}{w}_{ij}\in G\\ i\ne j\end{array}}{w}_{i,j}}$	Measures the connectedness of a network in terms of network's density, where pkl is the number of shortest paths between nodes k and l and $p_{kl}^j$ is the number of shortest paths between k and l that pass through node j
k	Degree	$k_i={\displaystyle \sum _{j\in V}{a}_{ij}}$	Number of neighbors connected to a node (hub metric)
BC	Betweenness centrality	$B{C}_i={\displaystyle \sum _{\begin{array}{c}k,l\in V\\ k\ne l, k\ne i, l\ne i\end{array}}\frac{p_{kl}^i}{p_{kl}}}$	Quantifies the importance of a node (hub metric)
ECC	Eccentricity	–	Indicates whether a node is central or peripheral in a network
d	Diameter	–	Maximum eccentricity
r	Radius	–	Minimum eccentricity
Lf	Leaf fraction	Lf = Nleaf/n−1	Fraction of nodes with degree equal to one
Th	Tree-hierarchy	$T_h=\frac{N_{leaf}}{2(n-1)B{C}_{max}}$	Quantifies the balance between diameter reduction and overload prevention
κ	Kappa or degree divergence	$\kappa =\frac{\langle k2\rangle }{\langle k\rangle }$	Measure of the broadness of the degree distribution
rdeg	Degree correlation	–	Quantifies the influence of a node's degree by its neighbors