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Modularity of Complex Networks Models

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Book cover Algorithms and Models for the Web Graph (WAW 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10088))

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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.

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Acknowledgements

This work is supported by Russian Science Foundation (grant number 16-11-10014), NSERC, The Tutte Institute for Mathematics and Computing, and Ryerson University.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Moscow, Russia

    Liudmila Ostroumova Prokhorenkova & Andrei Raigorodskii

  2. Yandex, Moscow, Russia

    Liudmila Ostroumova Prokhorenkova & Andrei Raigorodskii

  3. Ryerson University, Toronto, ON, Canada

    Paweł Prałat

  4. The Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada

    Paweł Prałat

  5. Moscow State University, Moscow, Russia

    Andrei Raigorodskii

  6. Buryat State University, Ulan-ude, Buryat Republic, Russia

    Andrei Raigorodskii

Authors
  1. Liudmila Ostroumova Prokhorenkova
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  2. Paweł Prałat
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  3. Andrei Raigorodskii
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Corresponding author

Correspondence to Liudmila Ostroumova Prokhorenkova .

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Editors and Affiliations

  1. Ryerson University, Toronto, Canada

    Anthony Bonato

  2. University of California San Diego, La Jolla, California, USA

    Fan Chung Graham

  3. Ryerson University, Toronto, Canada

    Paweł Prałat

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Ostroumova Prokhorenkova, L., Prałat, P., Raigorodskii, A. (2016). Modularity of Complex Networks Models. In: Bonato, A., Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2016. Lecture Notes in Computer Science(), vol 10088. Springer, Cham. https://doi.org/10.1007/978-3-319-49787-7_10

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  • DOI: https://doi.org/10.1007/978-3-319-49787-7_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49786-0

  • Online ISBN: 978-3-319-49787-7

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