Cycle Based Network Centrality.

Paths and cycles are the two pivotal elements in a network. Here, we demonstrate that paths, particularly the shortest ones, are incomplete in information network. However, based on such paths, many network centrality measures are designed. While extensive explorations on paths have been made, modest studies focus on the cycles on measuring network centrality. We study the relationship between the shortest cycle and the shortest path from extensive real-world networks. The results illustrate the incompleteness of the shortest paths on measuring network centrality. Noticing that the shortest cycle is much more robust than the shortest path, we propose two novel cycle-based network centrality measures to address the incompleteness of paths: the shortest cycle closeness centrality (SCC) and the all cycle betweenness centrality (ACC). Notwithstanding we focus on the network centrality problem, our findings on cycles can be applied to explain the incompleteness of paths in applications and could improve the applicability into more scenarios where the paths are employed in network science.