Many networks, such as transportation, power, and water distribution, can be
represented as graphs. Crucial challenge in graph representations is
identifying the importance of graph edges and their influence on overall
network efficiency and information flow performance. For example, important
edges in a transportation network are those roads that, when affected, will
significantly alter the network's overall efficiency. Commonly used approach to
finding such important edges is ``edge betweenness centrality'' (EBC), an edge
ranking measure to determine the influential edges of the graph based on
connectivity and information spread. Computing the EBC utilizing the common
Brandes algorithm involves calculating the shortest paths for every node pair,
which can be computationally expensive and restrictive, especially for large
graphs. Changes in the graph parameters, e.g., in the edge weight or the
addition and deletion of nodes or edges, require the recalculation of the EBC.
As the main contribution, we propose an approximate method to estimate the EBC
using a Graph Neural Network (GNN), a deep learning-based approach. We show
that it is computationally efficient compared to the conventional method,
especially for large graphs. The proposed method of GNN-based edge ranking is
evaluated on several synthetic graphs and a real-world transportation data set.
We show that this framework can estimate the approximate edge ranking much
faster compared to the conventional method. This approach is inductive, i.e.,
training and testing are performed on different sets of graphs with varying
numbers of nodes and edges. The proposed method is especially suitable for
applications on large-scale networks when edge information is desired, for
example, in urban infrastructure improvement projects, power, and water network
resilience analyses, and optimizing resource allocations in engineering
networks.

该文章提出一种基于图神经网络的边缘排序方法，用于评估不同边缘连接的重要性，并在大规模网络中表现出高效和准确的性能，此方法特别适用于城市基础设施的改进、电力和水资源网络的弹性分析以及工程网络的资源分配优化。