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

Naoki Masuda*, Hiroyoshi Miwa, Norio Konno

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Citations (Scopus)


Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabási 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.

Original languageEnglish
Article number036108
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
Publication statusPublished - 2005 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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