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: