Network accessibility as the emergence of cliques

We propose a topological formulation of accessibility based on the notion of Access Graph, in which two nodes are connected if they are reachable within a given travel time. We trace the emergence and evolution of its subgraphs with imposed levels of connectedness, specifically maximal clique and k-cores. We propose two complementary sets of accessibility indicators, cumulative and threshold, based on integral measures of subgraph growth and times at emergence of k-cores, respectively. For a meaningful comparison of networks across different dimensions, we contrast the realised accessibility with that of an idealised network on the same set of nodes. The proposed measures offer a view of accessibility that extends beyond the commonly used node-averaged indicators. Empirical analysis of 42 metro networks worldwide demonstrates universal patterns of accessibility behaviour. We illustrate the practical application of this approach on a case study where we examine the accessibility impacts yielded by alternative infrastructure and service developments. Our results amount to the reconceptualisation of accessibility within the complex network framework.