2015/05/20 by Jeannette Janssen, Janssen, Jeannette, Paweł Prałat +3
Computer Science · Physics and Astronomy · Social Sciences · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Human Mobility and Location-Based Analysis #Opportunistic and Delay-Tolerant Networks #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.1506.06053
openalex publication_date 2015/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spatial preferential attachment (SPA) is a model for complex networks. In\nthe SPA model, nodes are embedded in a metric space, and each node has a sphere\nof influence whose size increases if the node gains an in-link, and otherwise\ndecreases with time. In this paper, we study the behaviour of the SPA model\nwhen the distribution of the nodes is non-uniform. Specifically, the space is\ndivided into dense and sparse regions, where it is assumed that the dense\nregions correspond to coherent communities. We prove precise theoretical\nresults regarding the degree of a node, the number of common neighbours, and\nthe average out-degree in a region. Moreover, we show how these theoretically\nderived results about the graph properties of the model can be used to\nformulate a reliable estimator for the distance between certain pairs of nodes,\nand to estimate the density of the region containing a given node.\n