2002/11/18 by Bartolo Luque, Octavio Miramontes, Miramontes Octavio
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Complex network #Data Visualization and Analytics #Discrete mathematics #Geometry #Graph #Heterogeneous random walk in one dimension #Logarithm #Loop-erased random walk #Mathematical analysis #Mathematics #Physics #Random graph #Random walk #Scaling #Scaling law #Small-world network #Statistical physics #Statistics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1209/epl/i2003-00470-4
article, 7 figures
arxiv created 2002/11/18 · openalex publication_date 2003/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A parametrized family of random walks whose trajectories are easily identified as graphs is presented. This construction shows small-world–like behavior but, interestingly, a power law emerges between the minimal distance L and the number of nodes N of the graph instead of the typical logarithmic scaling. We explain this peculiar finding in the light of the well-known scaling relationships in Random Walk Theory. Our model establishes a link between Complex Networks and Self-Avoiding Random Walks, a useful theoretical framework in polymer science.