2007/09/04 by Oskar J. Sandberg, Oskar Sandberg, Sandberg, Oskar · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #60C05 #68R10 #68W20 #Advanced Clustering Algorithms Research #Combinatorics (math.CO) #Complex Network Analysis Techniques #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #cs.DS #math.CO #math.PR #msc:60C05 #msc:68R10 #msc:68W20
paper · pdf · doi:10.48550/arxiv.0709.0511
arxiv created 2007/09/04 · openalex publication_date 2007/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Graphs are called navigable if one can find short paths through them using only local knowledge. It has been shown that for a graph to be navigable, its construction needs to meet strict criteria. Since such graphs nevertheless seem to appear in nature, it is of interest to understand why these criteria should be fulfilled. In this paper we present a simple method for constructing graphs based on a model where nodes vertices are ``similar'' in two different ways, and tend to connect to those most similar to them - or cluster - with respect to both. We prove that this leads to navigable networks for several cases, and hypothesize that it also holds in great generality. Enough generality, perhaps, to explain the occurrence of navigable networks in nature.