A simple differential geometry for complex networks
Bibliographic Data
| ID | 6161569 |
|---|---|
| Authors | Emil Saucan (0000-0001-9033-0828, Max Planck Institute for Mathematics), Areejit Samal (0000-0002-6796-9604, Max Planck Institute for Mathematics), Jürgen Jost (0000-0001-5258-6590, Max Planck Institute for Mathematics) |
| Year | 2020 |
| Volume | 9 |
| Issue | S1 |
| Pages | S106-S133 |
| Publication date | 2020-11-16 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | PREPRINT |
| Venue | Network Science (JOURNAL) |
| Journal identifiers | ISSN: 2050-1250 • E-ISSN: 2050-1242 |
| Publisher | Cambridge University Press (PUBLISHER • US) |
| DOI | 10.1017/nws.2020.42 |
| OpenAlex | W3017715761 |
| Language | EN |
| Citations received | 1 |
| References cited | 49 |
We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particular, the proposed curvatures based on the interpretation of Haantjes definition as geodesic curvature allow us to give a network analogue of the classical local Gauss–Bonnet theorem. Furthermore, we propose even simpler and more intuitive proxies for the Haantjes curvature that allow for even faster and easier computations in large-scale networks. In addition, we also investigate the embedding properties of the proposed Ricci curvatures. Lastly, we also investigate the behavior, both on model and real-world networks, of the curvatures introduced herein with more established notions of Ricci curvature and other widely used network measures
Algorithm · Combinatorics · Computation · Curvature · Differential geometry · Embedding · Gaussian curvature · Geodesic · Geometry · Pure mathematics · Ricci curvature · Scalar curvature · Sectional curvature · Topology (electrical circuits · Computer Science · Geometric Analysis and Curvature Flows · Mathematics · Topological and Geometric Data Analysis · Artificial Intelligence
Networks
Graph evolution
Network Motifs
Statistical mechanics of complex networks
Collective dynamics of ‘small-world’ networks
Community structure in social and biological networks
Emergence of Scaling in Random Networks
A Set of Measures of Centrality Based on Betweenness
An Information Flow Model for Conflict and Fission in Small Groups
| Unique citing works | 1 |
|---|---|
| Citations per year | 0.2 |
| Citation span | 2021 - 2021 (1) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 1 |