Inflow and outflow centrality: novel centrality metrics inspired by graph convolution

Abstract Centrality metrics quantify a node’s importance within a network based on a node’s connectivity, path position, proximity to other nodes, or influence from neighbors. All of these properties are influenced by the network structure and do not consider a node’s features. To overcome this, two novel centrality metrics, termed inflow and outflow centrality, were introduced here. The metrics were derived from the aggregation approach used in graph convolutional networks, which allow for direct incorporation of node features with graph structure. The metrics were contrasted against the unweighted betweenness centrality and four node-weighted centrality metrics, weighted-degree, weighted-closeness, personalized PageRank, and alpha centrality, for an airport, an airplane trade, and a protein-protein interaction network. By emphasizing the contribution of otherwise little connected neighbor nodes, the new metrics prioritize nodes that are crucial to maintain a graph’s connectivity.