Modularity of Complex Networks Models View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2016

AUTHORS

Liudmila Ostroumova Prokhorenkova , Paweł Prałat , Andrei Raigorodskii

ABSTRACT

Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between vertices of different clusters. As a result, modularity is often used in optimization methods for detecting community structure in networks, and so it is an important graph parameter from practical point of view. Unfortunately, many existing non-spatial models of complex networks do not generate graphs with high modularity; on the other hand, spatial models naturally create clusters. We investigate this phenomenon by considering a few examples from both sub-classes. We prove precise theoretical results for the classical model of random d-regular graphs as well as the preferential attachment model, and contrast these results with the ones for the spatial preferential attachment (SPA) model that is a model for complex networks in which vertices are embedded in a metric space, and each vertex has a sphere of influence whose size increases if the vertex gains an in-link, and otherwise decreases with time. More... »

PAGES

115-126

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-49787-7_10

DOI

http://dx.doi.org/10.1007/978-3-319-49787-7_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033894459


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