Edge-based analysis of networks: Curvatures of graphs and hypergraphs
arXiv:2010.16366 · doi:10.1007/s12064-020-00328-0
Abstract
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of (hyper)edges, instead of vertices. For that purpose, we utilize so-called network curvatures. These curvatures quantify the local structural properties of (hyper)edges, that is, how, and how well, they are connected to others. In the case of directed networks, they assess the input they receive and the output they produce, and relations between them. With those tools, we can investigate biological networks. As examples, we apply our methods here to protein-protein interaction, transcriptional regulatory and metabolic networks.
arXiv comment12 pages, 6 figures
References in corpus (10)
- Mixing patterns in networks
- Networks beyond pairwise interactions: structure and dynamics
- Random hypergraphs and their applications
- Social contagion models on hypergraphs
- Forman curvature for complex networks
- Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
- Comparative analysis of two discretizations of Ricci curvature for complex networks
- Systematic evaluation of a new combinatorial curvature for complex networks
- Discrete Ricci curvatures for directed networks
- Degree difference: A simple measure to characterize structural heterogeneity in complex networks