2010/04/12 by G. Palla, Gergely Palla, László Lovász +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Assortativity #Biological network #Cluster analysis #Clustering coefficient #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Complex network #Computer science #Data mining #Degree distribution #Fractal #Generator (circuit theory) #Graph #Mathematics #Measure (data warehouse) #Multifractal system #Opinion Dynamics and Social Influence #Power (physics) #Theoretical computer science #math-ph #math.MP #physics.data-an #physics.soc-ph #stat.ME
paper · pdf · doi:10.1073/pnas.0912983107
published as Proc. Natl. Acad. Sci. USA 107: 7640-7645, (2010) · Preprint. Final version appeared in PNAS.
openalex publication_date 2010/04/12 · arxiv created 2010/04/29 · arxiv updated 2010/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed statistical properties, e.g., with degree or clustering coefficient distributions of various, very different forms. In turn, these graphs can be used to test hypotheses or as models of actual data. The method is based on a mapping between suitably chosen singular measures defined on the unit square and sparse infinite networks. Such a mapping has the great potential of allowing for graph theoretical results for a variety of network topologies. The main idea of our approach is to go to the infinite limit of the singular measure and the size of the corresponding graph simultaneously. A very unique feature of this construction is that with the increasing system size the generated graphs become topologically more structured. We present analytic expressions derived from the parameters of the--to be iterated--initial generating measure for such major characteristics of graphs as their degree, clustering coefficient, and assortativity coefficient distributions. The optimal parameters of the generating measure are determined from a simple simulated annealing process. Thus, the present work provides a tool for researchers from a variety of fields (such as biology, computer science, biology, or complex systems) enabling them to create a versatile model of their network data.