Graph Neural Networks for Fast Node Ranking Approximation

Abstract

Graphs arise naturally in numerous situations, including social graphs, transportation graphs, web graphs, protein graphs, etc. One of the important problems in these settings is to identify which nodes are important in the graph and how they affect the graph structure as a whole. Betweenness centrality and closeness centrality are two commonly used node ranking measures to find out influential nodes in the graphs in terms of information spread and connectivity. Both of these are considered as shortest path based measures as the calculations require the assumption that the information flows between the nodes via the shortest paths. However, exact calculations of these centrality measures are computationally expensive and prohibitive, especially for large graphs. Although researchers have proposed approximation methods, they are either less efficient or suboptimal or both. We propose the first graph neural network (GNN) based model to approximate betweenness and closeness centrality. In GNN, each node aggregates features of the nodes in multihop neighborhood. We use this feature aggregation scheme to model paths and learn how many nodes are reachable to a specific node. We demonstrate that our approach significantly outperforms current techniques while taking less amount of time through extensive experiments on a series of synthetic and real-world datasets. A benefit of our approach is that the model is inductive, which means it can be trained on one set of graphs and evaluated on another set of graphs with varying structures. Thus, the model is useful for both static graphs and dynamic graphs. Source code is available at https://github.com/sunilkmaurya/GNN_Ranking

Fast cluster-based computation of exact betweenness centrality in large graphs

“…Very recently, a Graph Neural Network (GNN) based model to approximate betweenness and closeness centrality has been proposed [31]. This work, among other similar ones [32], demonstrates that the efficient computation of the BC is a topic of great interest even in the field of deep learning and, particularly, graph neural networks.…”

GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks

“…(Rigutini et al, 2011) applies a neural network approach for preference learning, (Köppel et al, 2019) generalizes (Burges et al, 2005), but these methods require queries as input, which solve a different problem from ours. (Maurya et al, 2021) proposes the first GNN-based model to approximate betweenness and closeness centrality, facilitating locating influential nodes in the graphs in terms of information spread and connectivity. The pairwise direction is rarely considered in these works but it is important for the problem studied in this paper.…”

“…Moreover, there has been promising progress on combinatorial optimization in machine learning (Wang et al, 2021;Maurya et al, 2021), especially graph neural networks (GNNs) (Zhou et al, 2020;Wu et al, 2020), due to their potential in data exploration. Compared with its great success in many combinatorial tasks, the capability of GNNs in ranking tasks is still not well developed.…”

“…The few existing works are restricted to specific settings e.g. top-n personalized recommendations (Wang et al, 2021), approximating centrality measures (Maurya et al, 2021). Another technical gap is the inability to learn a model by directly optimizing the ranking objective, which we aim to fill in our work.…”

Identifying the Top-k Influential Spreaders in Social Networks: a Survey and Experimental Evaluation

“…Maurya et al [91] employed a graph neural network (GNN) for solving the betweenness and closeness approximation problem and outputting ranking scores for nodes. Nodes aggregate the nodes' features in their multi-hop neighborhood.…”