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Network quotients: structural skeletons of complex systems

Network quotients: structural skeletons of complex systems
Network quotients: structural skeletons of complex systems
A defining feature of many large empirical networks is their intrinsic complexity. However, many networks also contain a large degree of structural repetition. An immediate question then arises: can we characterize essential network complexity while excluding structural redundancy? In this article we utilize inherent network symmetry to collapse all redundant information from a network, resulting in a coarse graining which we show to carry the essential structural information of the “parent” network. In the context of algebraic combinatorics, this coarse-graining is known as the “quotient.” We systematically explore the theoretical properties of network quotients and summarize key statistics of a variety of “real-world” quotients with respect to those of their parent networks. In particular, we find that quotients can be substantially smaller than their parent networks yet typically preserve various key functional properties such as complexity (heterogeneity and hub vertices) and communication (diameter and mean geodesic distance), suggesting that quotients constitute the essential structural skeletons of their parent networks. We summarize with a discussion of potential uses of quotients in analysis of biological regulatory networks and ways in which using quotients can reduce the computational complexity of network algorithms
1539-3755
046102-[7pp]
Xiao, Yanghua
84781882-8b49-4f9d-9625-3757700e70da
MacArthur, Ben D.
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Wang, Hui
54e80ade-34fb-4d20-ae1f-41721a5300db
Xiong, Momiao
aac996e7-b3b5-4c4d-abcb-2c711778a671
Wang, Wei
85862755-49c9-4c7d-a1f4-d838d35cb7b7
Xiao, Yanghua
84781882-8b49-4f9d-9625-3757700e70da
MacArthur, Ben D.
2c0476e7-5d3e-4064-81bb-104e8e88bb6b
Wang, Hui
54e80ade-34fb-4d20-ae1f-41721a5300db
Xiong, Momiao
aac996e7-b3b5-4c4d-abcb-2c711778a671
Wang, Wei
85862755-49c9-4c7d-a1f4-d838d35cb7b7

Xiao, Yanghua, MacArthur, Ben D., Wang, Hui, Xiong, Momiao and Wang, Wei (2008) Network quotients: structural skeletons of complex systems. Physical Review E, 78 (4), 046102-[7pp]. (doi:10.1103/PhysRevE.78.046102). (PMID:18999488)

Record type: Article

Abstract

A defining feature of many large empirical networks is their intrinsic complexity. However, many networks also contain a large degree of structural repetition. An immediate question then arises: can we characterize essential network complexity while excluding structural redundancy? In this article we utilize inherent network symmetry to collapse all redundant information from a network, resulting in a coarse graining which we show to carry the essential structural information of the “parent” network. In the context of algebraic combinatorics, this coarse-graining is known as the “quotient.” We systematically explore the theoretical properties of network quotients and summarize key statistics of a variety of “real-world” quotients with respect to those of their parent networks. In particular, we find that quotients can be substantially smaller than their parent networks yet typically preserve various key functional properties such as complexity (heterogeneity and hub vertices) and communication (diameter and mean geodesic distance), suggesting that quotients constitute the essential structural skeletons of their parent networks. We summarize with a discussion of potential uses of quotients in analysis of biological regulatory networks and ways in which using quotients can reduce the computational complexity of network algorithms

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Published date: October 2008

Identifiers

Local EPrints ID: 175713
URI: http://eprints.soton.ac.uk/id/eprint/175713
ISSN: 1539-3755
PURE UUID: 0f639bd0-fd4c-4910-ae50-7d25c615b509
ORCID for Ben D. MacArthur: ORCID iD orcid.org/0000-0002-5396-9750

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Date deposited: 25 Feb 2011 14:17
Last modified: 14 Mar 2024 02:44

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Contributors

Author: Yanghua Xiao
Author: Hui Wang
Author: Momiao Xiong
Author: Wei Wang

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