Table 2 Graph theory metrics.

Clustering coefficient

A fraction of a node’s neighbors that are also neighbours of each other; a measure of clustered connectivity around individual nodes

\(C = \frac{1}{n}\sum\nolimits_{i \in n} {C_{i} } = \frac{1}{n}\sum\nolimits_{i \in n} {\frac{{2t_{i} }}{{k_{i} (k_{i} - 1)}}}\)

In the context of CT networks, it reflects uniformity of CT with respect to individual nodes

n = the total number of nodes

C_i = the clustering coefficient of node i

ki = the degree of node i

C_i = 0 for k_i < 2

Normalized clustering coefficient

Ratio of the mean clustering coefficient C and normalization factor C_rnad computed as the mean clustering coefficient of 10 random networks (see below) with the same number of nodes and edges as the tested input network

\(C_{norm} = \frac{C}{{C_{rand} }}\)

Characteristic pathlength

A measure of network integration representing the number of edges typically required to connect pairs of nodes in the network

\(L = \frac{1}{n}\sum\nolimits_{i \in N} {L_{i} } = \frac{1}{n}\sum\nolimits_{i \in N} {\frac{{\mathop \sum \nolimits_{j \in N \cdot j \ne i} d_{ij}^{ - 1} }}{n - 1}}\)

In the context of CT networks, path length represents the number of required indirect correlations surpassing the sparsity threshold

Li = the average distance between node i and all other nodes

d_ij = the distance from node i to node j

Normalized pathlength

The ratio of characteristic path length L and a normalization factor L_rnad based on 10 random networks, as described above

\(L_{norm} = \frac{L}{{L_{rand} }}\)

Small-world index

Describes a topology featuring numerous short-range connections with an admixture of few long-range connections; balances specialized and distributed processing while minimizing wiring costs. Small-world networks lie on a continuum between regular networks, in which each node has the same number of edges, and random networks, in which nodes are connected to other nodes with a random probability

\(S = \frac{{C_{norm} }}{{L_{norm} }}\)