Model-free hidden geometry of complex networks
arXiv:2011.08103 · doi:10.1103/PhysRevE.103.012305
Abstract
The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular methods employed in network embedding either rely on implicit approximations of the principle of proximity preservation or implement it by enforcing the geometry of the embedding space, thus hindering geometric properties that networks may spontaneously exhibit. Here, we take advantage of a model-free embedding method explicitly devised for preserving pairwise proximity, and characterize the geometry emerging from the mapping of several networks, both real and synthetic. We show that the learned embedding has simple and intuitive interpretations: the distance of a node from the geometric center is representative for its closeness centrality, and the relative positions of nodes reflect the community structure of the network. Proximity can be preserved in relatively low-dimensional embedding spaces, and the hidden geometry displays optimal performance in guiding greedy navigation regardless of the specific network topology. We finally show that the mapping provides a natural description of contagion processes on networks, with complex spatiotemporal patterns represented by waves propagating from the geometric center to the periphery. The findings deepen our understanding of the model-free hidden geometry of complex networks.
15 pages, 12 figures, 1 table
References in corpus (28)
- Community detection in graphs
- LINE: Large-scale Information Network Embedding
- Epidemic processes in complex networks
- Identification of influential spreaders in complex networks
- Graph Embedding Techniques, Applications, and Performance: A Survey
- The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
- Vital nodes identification in complex networks
- Hyperbolic Geometry of Complex Networks
- Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec
- Popularity versus Similarity in Growing Networks
- Navigability of Complex Networks
- Sustaining the Internet with Hyperbolic Mapping
- A small-world of weak ties provides optimal global integration of self-similar modules in functional brain networks
- Localization and centrality in networks
- Robust network community detection using balanced propagation
- Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space
- Emergent Hyperbolic Network Geometry
- Hidden geometric correlations in real multiplex networks
- Emergence of Soft Communities from Geometric Preferential Attachment
- Network Geometry Inference using Common Neighbors
- Navigable Networks as Nash Equilibria of Navigation Games
- Predicting the speed of epidemics spreading on networks
- Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks
- Diffusion geometry unravels the emergence of functional clusters in collective phenomena
- Characterizing the analogy between hyperbolic embedding and community structure of complex networks
- Navigability evaluation of complex networks by greedy routing efficiency
- k-core structure of real multiplex networks
- Network depth: identifying median and contours in complex networks