Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction

Masaki AIDA; Chisa TAKANO; Masayuki MURATA

doi:10.1587/transcom.2017EBN0001

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Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction

Masaki AIDA, Chisa TAKANO, Masayuki MURATA

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This paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.

Publication: IEICE TRANSACTIONS on Communications Vol.E101-B No.1 pp.123-136

Publication Date: 2018/01/01

Publicized: 2017/07/03

Online ISSN: 1745-1345

DOI: 10.1587/transcom.2017EBN0001

Type of Manuscript: POSITION PAPER

Category: Fundamental Theories for Communications

Authors

Masaki AIDA
  Tokyo Metropolitan University
Chisa TAKANO
  Hiroshima City University
Masayuki MURATA
  Osaka University

Keyword

spectral graph theory, coupled oscillators, node centrality, resonance, flaming, quantum theory

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Masaki AIDA, Chisa TAKANO, Masayuki MURATA, "Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction" in IEICE TRANSACTIONS on Communications, vol. E101-B, no. 1, pp. 123-136, January 2018, doi: 10.1587/transcom.2017EBN0001.
Abstract: This paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.
URL: https://globals.ieice.org/en_transactions/communications/10.1587/transcom.2017EBN0001/_p

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@ARTICLE{e101-b_1_123,
author={Masaki AIDA, Chisa TAKANO, Masayuki MURATA, },
journal={IEICE TRANSACTIONS on Communications},
title={Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction},
year={2018},
volume={E101-B},
number={1},
pages={123-136},
abstract={This paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.},
keywords={},
doi={10.1587/transcom.2017EBN0001},
ISSN={1745-1345},
month={January},}

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TY - JOUR
TI - Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction
T2 - IEICE TRANSACTIONS on Communications
SP - 123
EP - 136
AU - Masaki AIDA
AU - Chisa TAKANO
AU - Masayuki MURATA
PY - 2018
DO - 10.1587/transcom.2017EBN0001
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E101-B
IS - 1
JA - IEICE TRANSACTIONS on Communications
Y1 - January 2018
AB - This paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.
ER -