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The social graph based on real data

Tomasz M. Gwizdałła, Aleksandra Piecuch

TL;DR

This work addresses constructing a realistic social topology from empirical demographic data rather than online networks. It introduces a multi-level, undirected social-graph model derived from Polish statistics (GUS), focusing on households and close social groups, with schools and workplaces forming higher-level cliques and a Poisson-based mechanism for smaller groupings. The approach yields connected graphs that reflect real-world constraints and avoids hub-dominated degree distributions. Empirical analysis across graph sizes from $10^3$ to $10^6$ reveals a power-law-like tail in the degree distribution with exponents around $8$–$11$, a roughly logarithmic scaling of radius and diameter, and a clustering coefficient that remains nearly constant with size, signaling small-world structure. These findings demonstrate the model's potential for realistic simulations of social processes and inform future extensions to incorporate hubs and alternative connection architectures.

Abstract

In this paper, we propose a model enabling the creation of a social graph corresponding to real society. The procedure uses data describing the real social relations in the community, like marital status or number of kids. Results show the power-law behavior of the distribution of links and, typical for small worlds, the independence of the clustering coefficient on the size of the graph.

The social graph based on real data

TL;DR

This work addresses constructing a realistic social topology from empirical demographic data rather than online networks. It introduces a multi-level, undirected social-graph model derived from Polish statistics (GUS), focusing on households and close social groups, with schools and workplaces forming higher-level cliques and a Poisson-based mechanism for smaller groupings. The approach yields connected graphs that reflect real-world constraints and avoids hub-dominated degree distributions. Empirical analysis across graph sizes from to reveals a power-law-like tail in the degree distribution with exponents around –, a roughly logarithmic scaling of radius and diameter, and a clustering coefficient that remains nearly constant with size, signaling small-world structure. These findings demonstrate the model's potential for realistic simulations of social processes and inform future extensions to incorporate hubs and alternative connection architectures.

Abstract

In this paper, we propose a model enabling the creation of a social graph corresponding to real society. The procedure uses data describing the real social relations in the community, like marital status or number of kids. Results show the power-law behavior of the distribution of links and, typical for small worlds, the independence of the clustering coefficient on the size of the graph.
Paper Structure (2 sections, 3 figures)

This paper contains 2 sections, 3 figures.

Table of Contents

  1. Introduction and Model
  2. Results and Conclusions

Figures (3)

  • Figure 1: The comparison of links distribution histograms for different graph sizes. The solid lines, created for selected set of graph sizes ($10^3$, $10^4$,$10^5$,$10^6$) correspond the power-law dependencies and the colors correspond to the color of marker for particular size of community.
  • Figure 2: The dependence of radii and diameters on the size of community for graphs created according to the presented procedure.
  • Figure 3: The dependence of clustering coefficient on the size of community for graphs created according to the presented procedure. The values were obtained in the same wat as those from Fig.\ref{['f1_radius']}.