Node Centrality Based on Edge Dynamics in a Chaotic Network

This paper introduces a novel node centrality index based on edge dynamics in a complex network: adjacent edge index. Through the analysis of network dynamics and topology, we provide a neat index to qualify node importance, which is calculated by the eigenvector components corresponding to the Fiedler value of the network. Notably, it identifies nodes whose adjacent edge sets play a significant role in network synchronization. The index indicates that not only a node's degree but also its location should be considered. To demonstrate the effectiveness of the proposed index, consider a double-star network and a Jazz Musicians network in which chaotic Chua's circuits as nodes are coupled. By factoring in the dynamic information exchange between nodes and their neighbors, this index offers valuable insights for optimizing strategies in engineering areas such as efficient information dissemination.