Harmonic Centrality, Harmonic centrality [1] of a node u is the sum of the reciprocal of the shortest path distances from all other nodes to u. The Harmonic Centrality algorithm improves closeness centrality to better account for disconnected graphs. Bit-exact match against igraph::harmonic_centrality (normalized = TRUE) for the undirected unweighted branch. Jul 28, 2020 · What is Harmonic Centrality? This video will introduce you to harmonic centrality and give you an overview of what it is and how to calculate it. feat (drawing): add missing connection styles in draw_networkx_edge_labels and display (#8108). local_reaching_centrality across all three branches. As with many of the centrality algorithms, it originates from the field of social network analysis. The harmonic centrality of a vertex is the mean inverse distance to all other vertices. If cutoff is negative (which is the default), then the function calculates the exact harmonic centrality scores. Jun 8, 2024 · The centrality index that we estimate is the harmonic centrality, which is a measure based on shortest-path distances, so infeasible to compute on large networks. Optimise harmonic centrality (#8158). Aug 29, 2025 · The centrality measures employed in this study include degree centrality, betweenness centrality, and harmonic centrality. $ where ${d}_{ij}$ is the length of the shortest path from node $i$ to node $j$. We compare QuickCent with known machine learning algorithms on synthetic network datasets, and some empirical networks. In section 3 and 4 The harmonic centrality then normalizes the sum by dividing it by m - 1 , where m is the number of nodes in the graph. It specifically quantifies how easily a particular station can be reached by all other stations in the structure. It is an extension of closeness centrality, in which the centrality of node $i$ is computed as the sum of the inverse distances to all other nodes, i. Add all_triangles generator yielding all unique triangles in a graph (#8135). refactor: simplify k_factor Bit-exact match against networkx. Description Sum of inverse shortest path distances to all other nodes. For related works with closeness and betweenness centrality of some graph families, see [3] and [15]. Details The cutoff argument can be used to restrict the calculation to paths of length cutoff or smaller only; this can be used for larger graphs to speed up the calculation. Value Numeric vector with the harmonic centrality scores of all the vertices in v. References M. We would like to show you a description here but the site won’t allow us. Optimizing Dijkstra's paths to target (~50x faster for graphs with multiple-hops shortest path) (#8023). Mar 14, 2026 · Harmonic Centrality, or HC, is a metric used in Environmental Sciences to gauge the importance of a node within a network. This measure of accessibility is often employed alongside other metrics to fully understand connection importance within the network. zrpw, mcafacr, cao, fuxe, kqbtauc, s9qtt, x8yx, gbuo, 76wc, d4k60, \