Algebraic-graphical approach for signed dynamical networks

Guodong Shi; Claudio Altafini; John S. Baras

doi:10.1109/CDC.2017.8263943

Algebraic-graphical approach for signed dynamical networks

Guodong Shi, Claudio Altafini, John S. Baras

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two types of interactions are defined along the positive and negative links, respectively, arise from various biological, social, political, and economical systems. Starting from standard consensus dynamics, there are two basic types of negative interactions along negative links, namely state flipping or relative-state flipping. In this paper, we provide an algebraic-graphical method serving as a systematic tool of studying these dynamics over signed networks. Utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions, we show this method is useful to establish a series of basic convergence results for dynamics over signed networks.

Original language	English
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2009-2014
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8263943
Publication status	Published - 28 Jun 2017
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: 12 Dec 2017 → 15 Dec 2017

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Conference

Conference	56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 15/12/17

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10.1109/CDC.2017.8263943

Cite this

Shi, G., Altafini, C., & Baras, J. S. (2017). Algebraic-graphical approach for signed dynamical networks. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 2009-2014). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8263943

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title = "Algebraic-graphical approach for signed dynamical networks",

abstract = "A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two types of interactions are defined along the positive and negative links, respectively, arise from various biological, social, political, and economical systems. Starting from standard consensus dynamics, there are two basic types of negative interactions along negative links, namely state flipping or relative-state flipping. In this paper, we provide an algebraic-graphical method serving as a systematic tool of studying these dynamics over signed networks. Utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions, we show this method is useful to establish a series of basic convergence results for dynamics over signed networks.",

author = "Guodong Shi and Claudio Altafini and Baras, {John S.}",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.; 56th IEEE Annual Conference on Decision and Control, CDC 2017 ; Conference date: 12-12-2017 Through 15-12-2017",

year = "2017",

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doi = "10.1109/CDC.2017.8263943",

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Shi, G, Altafini, C & Baras, JS 2017, Algebraic-graphical approach for signed dynamical networks. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 2009-2014, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8263943

Algebraic-graphical approach for signed dynamical networks. / Shi, Guodong; Altafini, Claudio; Baras, John S.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 2009-2014 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two types of interactions are defined along the positive and negative links, respectively, arise from various biological, social, political, and economical systems. Starting from standard consensus dynamics, there are two basic types of negative interactions along negative links, namely state flipping or relative-state flipping. In this paper, we provide an algebraic-graphical method serving as a systematic tool of studying these dynamics over signed networks. Utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions, we show this method is useful to establish a series of basic convergence results for dynamics over signed networks.

AB - A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two types of interactions are defined along the positive and negative links, respectively, arise from various biological, social, political, and economical systems. Starting from standard consensus dynamics, there are two basic types of negative interactions along negative links, namely state flipping or relative-state flipping. In this paper, we provide an algebraic-graphical method serving as a systematic tool of studying these dynamics over signed networks. Utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions, we show this method is useful to establish a series of basic convergence results for dynamics over signed networks.

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M3 - Conference contribution

T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

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EP - 2014

BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017

Y2 - 12 December 2017 through 15 December 2017

ER -

Algebraic-graphical approach for signed dynamical networks

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