Edge ranking in a transport graph of Petrozavodsk basing on equilibrium flows

Game-theoretic methods are frequently used to model the dynamic processes in urban road networks and evaluate network efficiency. One of the key concepts in this field is a Wardrop equilibrium (user equilibrium), the situation where no driver can reduce their journey time by unilaterally choosing another route. The concept is widely used in the literature to model the distribution of regular trips in a transport network. In general case, the equilibrium is unstable, and the construction of a new equilibrium trip distribution may require significant time. At the same time, when analyzing transport networks, one is often interested in the impact of short-term changes, when a road is closed for a short time, and the drivers do not seek for a new equilibrium but rather select acceptable routes in the current situation. Here, Wardrop equilibrium can be seen as the basic flow distribution, and the temporal changes in agents' strategies have some impact on local or global characteristics of the network. One may predict the scale of this impact by estimating the importance of the edge being temporarily unavailable. In this work, we analyze edge centralities within a Wardrop equilibrium in the transport graph of Petrozavodsk. We propose a modification of edge betweenness centrality that incorporates precalculated equilibrium flows passing through the road segment. We illustrate how the resulting edge ranking can be used to enhance the classical betweenness centrality to consider not only the topological graph properties, but also the actual flow distribution. One can use the modified centrality measure to estimate the properties of Wardrop equilibrium and to increase the efficiency of its recalculation upon graph modifications. The results can be used in the traffic analysis and planning the development of the transport network.