Structural evolution of Ukraine's freight rail transportation system under partial network loss

Abstract

This paper employs the complex network theory methods to conduct a macro level investigation of the structural evolution of a freight railway transportation system under conditions of partial network loss, using the Ukrainian railway system as a case study. The autors conducted a comprehensive analysis of the statistical, spatial, and structural properties of graph-based representations of the network for the years 2013 and 2019. Initially, in 2013, the railway system exhibited characteristics typical of scale-free networks, as confirmed by statistical indicators. However, following the loss of 8.41% of track length and 21.55% of stations compared to the original network, the structural organization of freight wagon flows into trains lost its characteristic “heavy tail.” It was found that the empirical degree distribution of the network is better described by a truncated power-law model. The system shifted from the classical railway hub-and-spoke transportation model towards a more compact, point-to-point network structure, characterized by increasingly global connectivity. For the first time, it is demonstrated that the railway system's clustering coefficient increases under partial network loss, mirroring patterns observed in railway systems undergoing topological growth. It has been demonstrated that the structure of the network organizing the wagon flows in trains belongs to small-world networks. The results reveal structural transformations of the freight railway network after infrastructure losses, and confirm adaptive mechanisms that enable flow reorganisation under disruptive conditions. The obtained characteristics and revealed properties allow to reassess the strategies of resource allocation and management of railway systems in conditions of destructive influences on their infrastructure.