Structural position vectors and symmetries in complex networks

• DOI: 10.1063/5.0107583
• Publication Date: 2022-09-22T15:00:15Z
• Authors: Yong-Shang Long; Zheng-Meng Zhai; Ming Tang; Ying Liu; Ying-Cheng Lai
• Keywords: Position (finance); Similarity (geometry)

Symmetries, due to their fundamental importance dynamical processes on networks, have attracted a great deal of current research. Finding all symmetric nodes in large complex networks typically relies automorphism groups from algebraic-group theory, which are solvable quasipolynomial time. We articulate conceptually appealing and computationally extremely efficient approach finding characterizing by introducing structural position vector (SPV) for each node networks. establish the mathematical result that must same SPV value demonstrate, using six representative real world, these can be found linear Furthermore, SPVs not only characterize similarity but also quantify nodal influences propagation dynamics. A caveat is proved relating values symmetries sufficient; i.e., having may symmetric, arises regular or with dominant component. point out an analysis this is, fact, shared known existing approaches literature. further argue, aid analysis, our method generally effective real-world do Our SPV-based framework, therefore, provides physically intuitive way uncover, understand, exploit structures arising applications.