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

Betweenness centrality is an important measure to find out influential nodes in networks in terms of information spread and connectivity. However, the exact calculation of betweenness centrality is computationally expensive. Although researchers have proposed approximation methods, they are either less efficient, or suboptimal, or both. In this paper, we present a Graph Neural Network(GNN) based inductive framework which uses constrained message passing of node features to approximate betweenness centrality. As far as we know, we are the first to propose a GNN based model to accomplish this task. We demonstrate that our approach dramatically outperforms current techniques while taking less amount of time through extensive experiments on a series of real-world datasets.

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Graphs help to define the relationships between entities in the data. These relationships, represented by edges, often provide additional context information which can be utilised to discover patterns in the data. Graph Neural Networks (GNNs) employ the inductive bias of the graph structure to learn and predict on various tasks. The primary operation of graph neural networks is the feature aggregation step performed over neighbours of the node based on the structure of the graph. In addition to its own features, for each hop, the node gets additional combined features from its neighbours. These aggregated features help define the similarity or dissimilarity of the nodes with respect to the labels and are useful for tasks like node classification. However, in real-world data, features of neighbours at different hops may not correlate with the node's features. Thus, any indiscriminate feature aggregation by GNN might cause the addition of noisy features leading to degradation in model's performance. In this work, we show that selective aggregation of node features from various hops leads to better performance than default aggregation on the node classification task. Furthermore, we propose a Dual-Net GNN architecture with a classifier model and a selector model. The classifier model trains over a subset of input node features to predict node labels while the selector model learns to provide optimal input subset to the classifier for the best performance. These two models are trained jointly to learn the best subset of features that give higher accuracy in node label predictions. With extensive experiments, we show that our proposed model outperforms both feature selection methods and state-of-the-art GNN models with remarkable improvements up to 27.8%.