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Many networks, such as transportation, power, and water distribution, can berepresented as graphs. Crucial challenge in graph representations isidentifying the importance of graph edges and their influence on overallnetwork efficiency and information flow performance. For example, importantedges in a transportation network are those roads that, when affected, willsignificantly alter the network's overall efficiency. Commonly used approach tofinding such important edges is ``edge betweenness centrality'' (EBC), an edgeranking measure to determine the influential edges of the graph based onconnectivity and information spread. Computing the EBC utilizing the commonBrandes algorithm involves calculating the shortest paths for every node pair,which can be computationally expensive and restrictive, especially for largegraphs. Changes in the graph parameters, e.g., in the edge weight or theaddition and deletion of nodes or edges, require the recalculation of the EBC.As the main contribution, we propose an approximate method to estimate the EBCusing a Graph Neural Network (GNN), a deep learning-based approach. We showthat it is computationally efficient compared to the conventional method,especially for large graphs. The proposed method of GNN-based edge ranking isevaluated on several synthetic graphs and a real-world transportation data set.We show that this framework can estimate the approximate edge ranking muchfaster compared to the conventional method. This approach is inductive, i.e.,training and testing are performed on different sets of graphs with varyingnumbers of nodes and edges. The proposed method is especially suitable forapplications on large-scale networks when edge information is desired, forexample, in urban infrastructure improvement projects, power, and water networkresilience analyses, and optimizing resource allocations in engineeringnetworks.

Edge Ranking of Graphs in Transportation Networks using a Graph Neural Network (GNN)