where \(P_{n}\ \)is the accessibility matrix for the path
length n = 0,…, \(N\), \(\text{nnz}(P_{n})\) is the number of
non-zero elements of the accessibility matrix, and \(N\) is the number
of nodes in the network. In the upper limit of path density, i.e.\(p\left(P_{n}\right)=\ \)1, most nodes can reach each other. On the
contrary, for a low path density \(p\left(P_{n}\right)=\ \)0 the
network tends to be temporarily disconnected ( Lentz et al., 2016)
Causal fidelity is calculated as the quotient of path densities, defined
as: