A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions

A. Newton Licciardi Jr.; L.H.A. Monteiro; A. Newton Licciardi Jr.; L.H.A. Monteiro

doi:10.3934/mbe.2024211

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 4801-4813. doi: 10.3934/mbe.2024211

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Research article

A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions

A. Newton Licciardi Jr. ^1,2,
L.H.A. Monteiro ^{1,2
,
,}

1.
Universidade de São Paulo, Escola Politécnica, São Paulo, SP, Brazil
2.
Universidade Presbiteriana Mackenzie, Escola de Engenharia, São Paulo, SP, Brazil

Received: 08 October 2023 Revised: 10 December 2023 Accepted: 02 February 2024 Published: 29 February 2024

Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.
- complex network,
- power law,
- scale free,
- small world,
- social interaction
Citation: A. Newton Licciardi Jr., L.H.A. Monteiro. A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 4801-4813. doi: 10.3934/mbe.2024211

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Abstract

Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.

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