Network Size Reduction Preserving Optimal Modularity and Clique
Partition

D 2022

Network Size Reduction Preserving Optimal Modularity and Clique Partition

BELY, Aliaksandr and Stanislav SOBOLEVSKY

Basic information

Original name

Network Size Reduction Preserving Optimal Modularity and Clique Partition

Authors

BELY, Aliaksandr (112 Belarus, guarantor, belonging to the institution) and Stanislav SOBOLEVSKY (112 Belarus, belonging to the institution)

Edition

Cham, Lecture Notes in Computer Science, p. 19-33, 15 pp. 2022

Publisher

Springer, Cham

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10102 Applied mathematics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

URL

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14310/22:00128549

Organization unit

Faculty of Science

ISBN

978-3-031-10521-0

ISSN

DOI

http://dx.doi.org/10.1007/978-3-031-10522-7_2

UT WoS

000916469700002

Keywords in English

Network size reduction Clustering Community detection Modularity Clique partitioning problem Exact solution

Abstract

V originále

Graph clustering and community detection are significant and actively developing topics in network science. Uncovering community structure can provide essential information about the underlying system. In this work, we consider two closely related graph clustering problems. One is the clique partitioning problem, and the other is the maximization of partition quality function called modularity. We are interested in the exact solution. However, both problems are NP-hard. Thus the computational complexity of any existing algorithm makes it impossible to solve the problems exactly for the networks larger than several hundreds of nodes. That is why even a small reduction of network size can significantly improve the speed of finding the solution to these problems. We propose a new method for reducing the network size that preserves the optimal partition in terms of modularity score or the clique partitioning objective function. Furthermore, we prove that the optimal partition of the reduced network has the same quality as the optimal partition of the initial network. We also address the cases where a previously proposed method could provide incorrect results. Finally, we evaluate our method by finding the optimal partitions for two sets of networks. Our results show that the proposed method reduces the network size by 40% on average, decreasing the computation time by about 54%.

Links

MUNI/J/0008/2021, interní kód MU

Name: Digital City

Investor: Masaryk University, MASH JUNIOR - MUNI Award In Science and Humanities JUNIOR

Citovat

BELY, Aliaksandr and Stanislav SOBOLEVSKY. Network Size Reduction Preserving Optimal Modularity and Clique Partition. In Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. Lecture Notes in Computer Science. Cham: Springer, Cham, 2022, p. 19-33. ISBN 978-3-031-10521-0. Available from: https://dx.doi.org/10.1007/978-3-031-10522-7_2.

@inproceedings{2252583,
   author = {Bely, Aliaksandr and Sobolevsky, Stanislav},
   address = {Cham},
   booktitle = {Lecture Notes in Computer Science},
   doi = {http://dx.doi.org/10.1007/978-3-031-10522-7_2},
   editor = {Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O.},
   keywords = {Network size reduction Clustering Community detection Modularity Clique partitioning problem Exact solution},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Cham},
   isbn = {978-3-031-10521-0},
   pages = {19-33},
   publisher = {Springer, Cham},
   title = {Network Size Reduction Preserving Optimal Modularity and Clique Partition},
   url = {https://doi.org/10.1007/978-3-031-10522-7_2},
   year = {2022}
}

TY  - JOUR
ID  - 2252583
AU  - Bely, Aliaksandr - Sobolevsky, Stanislav
PY  - 2022
TI  - Network Size Reduction Preserving Optimal Modularity and Clique Partition
PB  - Springer, Cham
CY  - Cham
SN  - 9783031105210
KW  - Network size reduction Clustering Community detection Modularity Clique partitioning problem Exact solution
UR  - https://doi.org/10.1007/978-3-031-10522-7_2
N2  - Graph clustering and community detection are significant and actively developing topics in network science. Uncovering community structure can provide essential information about the underlying system. In this work, we consider two closely related graph clustering problems. One is the clique partitioning problem, and the other is the maximization of partition quality function called modularity. We are interested in the exact solution. However, both problems are NP-hard. Thus the computational complexity of any existing algorithm makes it impossible to solve the problems exactly for the networks larger than several hundreds of nodes. That is why even a small reduction of network size can significantly improve the speed of finding the solution to these problems. We propose a new method for reducing the network size that preserves the optimal partition in terms of modularity score or the clique partitioning objective function. Furthermore, we prove that the optimal partition of the reduced network has the same quality as the optimal partition of the initial network. We also address the cases where a previously proposed method could provide incorrect results. Finally, we evaluate our method by finding the optimal partitions for two sets of networks. Our results show that the proposed method reduces the network size by 40% on average, decreasing the computation time by about 54%.
ER  -

BELY, Aliaksandr and Stanislav SOBOLEVSKY. Network Size Reduction Preserving Optimal Modularity and Clique Partition. In Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. \textit{Lecture Notes in Computer Science}. Cham: Springer, Cham, 2022, p.~19-33. ISBN~978-3-031-10521-0. Available from: https://dx.doi.org/10.1007/978-3-031-10522-7\_{}2.

Detailed Information on Publication Record