Geographical threshold graphs with small-world and scale-free properties

Abstract

Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabasi and Albert simultaneously reproduces these properties, and geographical versions of growing networks have also been analyzed. However, nongrowing networks with intrinsic vertex weights often explain these features more plausibly, since not all networks are really growing. We propose a geographical nongrowing network model with vertex weights. Edges are assumed to form when a pair of vertices are spatially close and/or have large summed weights. Our model generalizes a variety of models as well as the original nongeographical counterpart, such as the unit disk graph, the Boolean model, and the gravity model, which appear in the contexts of percolation, wire communication, mechanical and solid physics, sociology, economy, and marketing. In appropriate configurations, our model produces small-world networks with power-law degree distributions. We also discuss the relation between geography, power laws in networks, and power laws in general quantities serving as vertex weights.

26 pages (double-space format, including 4 figures)

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Cited by in corpus (26)

• Spatial Networks
• Trainspotting: Extraction and Analysis of Traffic and Topologies of Transportation Networks
• The effects of spatial constraints on the evolution of weighted complex networks
• Superlinear and sublinear urban scaling in geographical network model of the city
• VIP-club phenomenon: emergence of elites and masterminds in social networks
• Crossovers in ScaleFree Networks on Geographical Space
• Introduction to correlation networks: Interdisciplinary approaches beyond thresholding
• Growing networks under geographical constraints
• Scale-free networks embedded in fractal space
• Random geometric graph description of connectedness percolation in rod systems
• Rigorous results on the threshold network model
• Contact graphs of disk packings as a model of spatial planar networks
• Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory
• Epidemic dynamics on metapopulation networks with node2vec mobility
• Generalised thresholding of hidden variable network models with scale-free property
• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Metapopulation models imply non-Poissonian statistics of interevent times
• Threshold graph limits and random threshold graphs
• Solvable Metric Growing Networks
• Spectral Properties of the Threshold Network Model
• Generalized Erdos Numbers for network analysis
• Logistic dynamics of small populations with demographic stochasticity
• Statistical properties of a generalized threshold network model
• Connectivity and giant component in random distance graphs
• On the Mixing Time of Geographical Threshold Graphs
• Factorization threshold models for scale-free networks generation