1
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Ramirez LS, Vazquez F, San Miguel M, Galla T. Ordering dynamics of nonlinear voter models. Phys Rev E 2024; 109:034307. [PMID: 38632723 DOI: 10.1103/physreve.109.034307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 02/14/2024] [Indexed: 04/19/2024]
Abstract
We study the ordering dynamics of nonlinear voter models with multiple states, also providing a discussion of the two-state model. The rate with which an individual adopts an opinion scales as the qth power of the number of the individual's neighbors in that state. For q>1 the dynamics favor the opinion held by the most agents. The ordering to consensus is driven by deterministic drift, and noise plays only a minor role. For q<1 the dynamics favors minority opinions, and for multistate models the ordering proceeds through a noise-driven succession of metastable states. Unlike linear multistate systems, the nonlinear model cannot be reduced to an effective two-state model. We find that the average density of active interfaces in the model with multiple opinion states does not show a single exponential decay in time for q<1, again at variance with the linear model. This highlights the special character of the conventional (linear) voter model, in which deterministic drift is absent. As part of our analysis, we develop a pair approximation for the multistate model on graphs, valid for any positive real value of q, improving on previous approximations for nonlinear two-state voter models.
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Affiliation(s)
- Lucía S Ramirez
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Federico Vazquez
- Instituto de Cálculo, FCEyN, Universidad de Buenos Aires and CONICET, Intendente Guiraldes 2160, Cero + Infinito, Buenos Aires C1428EGA, Argentina
| | - Maxi San Miguel
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Tobias Galla
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
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2
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Min B, San Miguel M. Threshold Cascade Dynamics in Coevolving Networks. ENTROPY (BASEL, SWITZERLAND) 2023; 25:929. [PMID: 37372273 DOI: 10.3390/e25060929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 06/08/2023] [Accepted: 06/09/2023] [Indexed: 06/29/2023]
Abstract
We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state such as a new opinion, idea, or innovation and the network plasticity, implemented as the rewiring of links to cut the connections between nodes in different states. Using numerical simulations and a mean-field theoretical analysis, we demonstrate that the coevolutionary dynamics can significantly affect the cascade dynamics. The domain of parameters, i.e., the threshold and mean degree, for which global cascades occur shrinks with an increasing network plasticity, indicating that the rewiring process suppresses the onset of global cascades. We also found that during evolution, non-adopting nodes form denser connections, resulting in a wider degree distribution and a non-monotonous dependence of cascades sizes on plasticity.
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Affiliation(s)
- Byungjoon Min
- Department of Physics, Chungbuk National University, Cheongju 28644, Chungbuk, Republic of Korea
- Research Institute for Nanoscale Science and Technology, Chungbuk National University, Cheongju 28644, Chungbuk, Republic of Korea
| | - Maxi San Miguel
- IFISC (CSIC-UIB), Institute for Cross-Disciplinary Physics and Complex Systems, Campus Universitat Illes Balears, E-07122 Palma, Spain
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3
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Cosenza MG, Herrera-Diestra JL. Coevolutionary Dynamics with Global Fields. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1239. [PMID: 36141125 PMCID: PMC9497736 DOI: 10.3390/e24091239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 08/24/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
We investigate the effects of external and autonomous global interaction fields on an adaptive network of social agents with an opinion formation dynamics based on a simple imitation rule. We study the competition between global fields and adaptive rewiring on the space of parameters of the system. The model represents an adaptive society subject to global mass media such as a directed opinion influence or feedback of endogenous cultural trends. We show that, in both situations, global mass media contribute to consensus and to prevent the fragmentation of the social network induced by the coevolutionary dynamics. We present a discussion of these results in the context of dynamical systems and opinion formation dynamics.
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Affiliation(s)
- Mario G. Cosenza
- School of Physical Sciences & Nanotechnology, Universidad Yachay Tech, Urcuquí 100115, Ecuador
| | - José L. Herrera-Diestra
- Department of Integrative Biology, University of Texas at Austin, Austin, TX 78712, USA
- Centro de Simulacion y Modelos (CeSiMo), Universidad de Los Andes, Mérida 5101, Venezuela
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4
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Jędrzejewski A, Sznajd-Weron K. Pair approximation for the q-voter models with quenched disorder on networks. Phys Rev E 2022; 105:064306. [PMID: 35854498 DOI: 10.1103/physreve.105.064306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2022] [Accepted: 05/19/2022] [Indexed: 06/15/2023]
Abstract
Using two models of opinion dynamics, the q-voter model with independence and the q-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of disorder lead to the same result in the q-voter model with anticonformity at the mean-field level, they do lead to distinct phase diagrams on networks. These phase diagrams shift towards each other as the average node degree of a network increases, and eventually, they coincide in the mean-field limit. In contrast, for the q-voter model with independence, the phase diagrams move towards the same direction regardless of the disorder type, and they do not coincide even in the mean-field limit. To validate our results, we carry out Monte Carlo simulations on random regular graphs and Barabási-Albert networks. Although the pair approximation may incorrectly predict the type of phase transitions for the annealed models, we have not observed such errors for their quenched counterparts.
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Affiliation(s)
- Arkadiusz Jędrzejewski
- Department of Theoretical Physics, Wrocław University of Science and Technology, Wrocław, Poland
| | - Katarzyna Sznajd-Weron
- Department of Theoretical Physics, Wrocław University of Science and Technology, Wrocław, Poland
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5
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Murase Y, Jo HH, Török J, Kertész J, Kaski K. Deep Learning Exploration of Agent-Based Social Network Model Parameters. Front Big Data 2021; 4:739081. [PMID: 34661097 PMCID: PMC8511694 DOI: 10.3389/fdata.2021.739081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Accepted: 09/14/2021] [Indexed: 11/17/2022] Open
Abstract
Interactions between humans give rise to complex social networks that are characterized by heterogeneous degree distribution, weight-topology relation, overlapping community structure, and dynamics of links. Understanding these characteristics of social networks is the primary goal of their research as they constitute scaffolds for various emergent social phenomena from disease spreading to political movements. An appropriate tool for studying them is agent-based modeling, in which nodes, representing individuals, make decisions about creating and deleting links, thus yielding various macroscopic behavioral patterns. Here we focus on studying a generalization of the weighted social network model, being one of the most fundamental agent-based models for describing the formation of social ties and social networks. This generalized weighted social network (GWSN) model incorporates triadic closure, homophilic interactions, and various link termination mechanisms, which have been studied separately in the previous works. Accordingly, the GWSN model has an increased number of input parameters and the model behavior gets excessively complex, making it challenging to clarify the model behavior. We have executed massive simulations with a supercomputer and used the results as the training data for deep neural networks to conduct regression analysis for predicting the properties of the generated networks from the input parameters. The obtained regression model was also used for global sensitivity analysis to identify which parameters are influential or insignificant. We believe that this methodology is applicable for a large class of complex network models, thus opening the way for more realistic quantitative agent-based modeling.
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Affiliation(s)
| | - Hang-Hyun Jo
- Department of Physics, The Catholic University of Korea, Bucheon, South Korea
| | - János Török
- Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, Hungary.,Department of Network and Data Science, Central European University, Vienna, Austria.,MTA-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Budapest, Hungary
| | - János Kertész
- Department of Network and Data Science, Central European University, Vienna, Austria.,Department of Computer Science, Aalto University, Espoo, Finland
| | - Kimmo Kaski
- Department of Computer Science, Aalto University, Espoo, Finland.,The Alan Turing Institute, British Library, London, United Kingdom
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Abstract
We extend the agent-based models for knowledge diffusion in networks, restricted to random mindless interactions and to “frozen” (static) networks, in order to take into account intelligent agents and network co-evolution. Intelligent agents make decisions under bounded rationality. This is the key distinction of intelligent interacting agents compared to mindless colliding molecules, involved in the usual diffusion mechanism resulting from accidental collisions. The co-evolution of link weights and knowledge levels is modeled at the local microscopic level of “agent-to-agent” interaction. Our network co-evolution model is actually a “learning mechanism”, where weight updates depend on the previous values of both weights and knowledge levels. The goal of our work is to explore the impact of (a) the intelligence of the agents, modeled by the selection-decision rule for knowledge acquisition, (b) the innovation rate of the agents, (c) the number of “top innovators” and (d) the network size. We find that rational intelligent agents transform the network into a “centralized world”, reducing the entropy of their selections-decisions for knowledge acquisition. In addition, we find that the average knowledge, as well as the “knowledge inequality”, grow exponentially.
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7
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Agarwal P, Simper M, Durrett R. The q-voter model on the torus. ELECTRON J PROBAB 2021. [DOI: 10.1214/21-ejp682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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8
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Promoters versus Adversaries of Change: Agent-Based Modeling of Organizational Conflict in Co-Evolving Networks. MATHEMATICS 2020. [DOI: 10.3390/math8122235] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The social adoption of change is usually hard because in reality, forces opposing the social adoption of change manifest. This situation of organizational conflict corresponds to the case where two competing groups of influential agents (“promoters” versus “adversaries” of change) operate concurrently within the same organizational network. We model and explore the co-evolution of interpersonal ties and attitudes in the presence of conflict, taking into account explicitly the microscopic “agent-to-agent” interactions. In this perspective, we propose a new ties-attitudes co-evolution model where the diffusion of attitudes depends on the weights and the evolution of weights is formulated as a “learning mechanism” (weight updates depend on the previous values of both weights and attitudes). As a result, the co-evolution is intrinsic/endogenous. We simulate representative scenarios of conflict in 4 real organizational networks. In order to formulate structural balance in directed networks, we extended Heider’s definition of balance considering directed triangles. The evolution of balance involves two stages: first, negative links pop up disorderly and destroy balance, but after some time, as new negative links are formed, a “new” balance is re-established. This “new” balance is emerging concurrently with the polarization of attitudes or domination of one attitude. Moreover, same-minded agents are positively linked and different-minded agents are negatively-linked. This macroscopic self-organization of the system is due only to agent-to-agent interactions, involving feedbacks on weight updates at the local microscopic level.
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Jędrzejewski A, Toruniewska J, Suchecki K, Zaikin O, Hołyst JA. Spontaneous symmetry breaking of active phase in coevolving nonlinear voter model. Phys Rev E 2020; 102:042313. [PMID: 33212744 DOI: 10.1103/physreve.102.042313] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 10/06/2020] [Indexed: 11/07/2022]
Abstract
We study an adaptive network model driven by a nonlinear voter dynamics. Each node in the network represents a voter and can be in one of two states that correspond to different opinions shared by the voters. A voter disagreeing with its neighbor's opinion may either adopt it or rewire its link to another randomly chosen voter with any opinion. The system is studied by means of the pair approximation in which a distinction between the average degrees of nodes in different states is made. This approach allows us to identify two dynamically active phases: a symmetric and an asymmetric one. The asymmetric active phase, in contrast to the symmetric one, is characterized by different numbers of nodes in the opposite states that coexist in the network. The pair approximation predicts the possibility of spontaneous symmetry breaking, which leads to a continuous phase transition between the symmetric and the asymmetric active phases. In this case, the absorbing transition occurs between the asymmetric active and the absorbing phases after the spontaneous symmetry breaking. Discontinuous phase transitions and hysteresis loops between both active phases are also possible. Interestingly, the asymmetric active phase is not displayed by the model where the rewiring occurs only to voters sharing the same opinion, studied by other authors. Our results are backed up by Monte Carlo simulations.
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Affiliation(s)
- Arkadiusz Jędrzejewski
- Department of Operations Research and Business Intelligence, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Joanna Toruniewska
- Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
| | - Krzysztof Suchecki
- Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
| | - Oleg Zaikin
- ITMO University, 49 Kronverkskiy av., 197101 Saint Petersburg, Russia
| | - Janusz A Hołyst
- Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland.,ITMO University, 49 Kronverkskiy av., 197101 Saint Petersburg, Russia
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10
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Raducha T, San Miguel M. Emergence of complex structures from nonlinear interactions and noise in coevolving networks. Sci Rep 2020; 10:15660. [PMID: 32973287 PMCID: PMC7519106 DOI: 10.1038/s41598-020-72662-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 09/03/2020] [Indexed: 11/14/2022] Open
Abstract
We study the joint effect of the non-linearity of interactions and noise on coevolutionary dynamics. We choose the coevolving voter model as a prototype framework for this problem. By numerical simulations and analytical approximations we find three main phases that differ in the absolute magnetisation and the size of the largest component: a consensus phase, a coexistence phase, and a dynamical fragmentation phase. More detailed analysis reveals inner differences in these phases, allowing us to divide two of them further. In the consensus phase we can distinguish between a weak or alternating consensus and a strong consensus, in which the system remains in the same state for the whole realisation of the stochastic dynamics. In the coexistence phase we distinguish a fully-mixing phase and a structured coexistence phase, where the number of active links drops significantly due to the formation of two homogeneous communities. Our numerical observations are supported by an analytical description using a pair approximation approach and an ad-hoc calculation for the transition between the coexistence and dynamical fragmentation phases. Our work shows how simple interaction rules including the joint effect of non-linearity, noise, and coevolution lead to complex structures relevant in the description of social systems.
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Affiliation(s)
- Tomasz Raducha
- Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland. .,IFISC, Institute for Cross-disciplinary Physics and Complex Systems (UIB-CSIC), Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spain.
| | - Maxi San Miguel
- IFISC, Institute for Cross-disciplinary Physics and Complex Systems (UIB-CSIC), Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spain
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11
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Kureh YH, Porter MA. Fitting in and breaking up: A nonlinear version of coevolving voter models. Phys Rev E 2020; 101:062303. [PMID: 32688568 DOI: 10.1103/physreve.101.062303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Accepted: 02/07/2020] [Indexed: 11/07/2022]
Abstract
We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic process. Most prior work on coevolving voter models has focused on linear update rules with fixed and homogeneous rewiring and adopting probabilities. By contrast, in our nonlinear version, the probability that a node rewires or adopts is a function of how well it "fits in" with the nodes in its neighborhood. To explore this idea, we incorporate a local-survey parameter σ_{i} that encodes the fraction of neighbors of an updating node i that share its opinion state. In an update, with probability σ_{i}^{q} (for some nonlinearity parameter q), the updating node rewires; with complementary probability 1-σ_{i}^{q}, the updating node adopts a new opinion state. We study this mechanism using three rewiring schemes: after an updating node deletes one of its discordant edges, it then either (1) "rewires-to-random" by choosing a new neighbor in a random process; (2) "rewires-to-same" by choosing a new neighbor in a random process from nodes that share its state; or (3) "rewires-to-none" by not rewiring at all (akin to "unfriending" on social media). We compare our nonlinear coevolving voter model to several existing linear coevolving voter models on various network architectures. Relative to those models, we find in our model that initial network topology plays a larger role in the dynamics and that the choice of rewiring mechanism plays a smaller role. A particularly interesting feature of our model is that, under certain conditions, the opinion state that is held initially by a minority of the nodes can effectively spread to almost every node in a network if the minority nodes view themselves as the majority. In light of this observation, we relate our results to recent work on the majority illusion in social networks.
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Affiliation(s)
- Yacoub H Kureh
- Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095, USA
| | - Mason A Porter
- Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095, USA
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12
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Teza G, Suweis S, Gherardi M, Maritan A, Cosentino Lagomarsino M. Network model of conviction-driven social segregation. Phys Rev E 2019; 99:032310. [PMID: 30999432 DOI: 10.1103/physreve.99.032310] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2018] [Indexed: 11/07/2022]
Abstract
To measure, predict, and prevent social segregation, it is necessary to understand the factors that cause it. While in most available descriptions space plays an essential role, one outstanding question is whether and how this phenomenon is possible in a well-mixed social network. We define and solve a simple model of segregation on networks based on discrete convictions. In our model, space does not play a role, and individuals never change their conviction, but they may choose to connect socially to other individuals based on two criteria: sharing the same conviction and individual popularity (regardless of conviction). The tradeoff between these two moves defines a parameter, analogous to the "tolerance" parameter in classical models of spatial segregation. We show numerically and analytically that this parameter determines a true phase transition (somewhat reminiscent of phase separation in a binary mixture) between a well-mixed and a segregated state. Additionally, minority convictions segregate faster and inter-specific aversion alone may lead to a segregation threshold with similar properties. Together, our results highlight the general principle that a segregation transition is possible in absence of spatial degrees of freedom, provided that conviction-based rewiring occurs on the same time scale of popularity rewirings.
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Affiliation(s)
- Gianluca Teza
- Dipartimento di Fisica e Astronomia G. Galilei, University of Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Samir Suweis
- Dipartimento di Fisica e Astronomia G. Galilei, University of Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Marco Gherardi
- Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia G. Galilei, University of Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Marco Cosentino Lagomarsino
- Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy.,IFOM, FIRC Institute for Molecular Oncology, Milan, Italy
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13
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Murase Y, Jo HH, Török J, Kertész J, Kaski K. Structural transition in social networks: The role of homophily. Sci Rep 2019; 9:4310. [PMID: 30867537 PMCID: PMC6416335 DOI: 10.1038/s41598-019-40990-z] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Accepted: 02/27/2019] [Indexed: 11/08/2022] Open
Abstract
We introduce a model for the formation of social networks, which takes into account the homophily or the tendency of individuals to associate and bond with similar others, and the mechanisms of global and local attachment as well as tie reinforcement due to social interactions between people. We generalize the weighted social network model such that the nodes or individuals have F features and each feature can have q different values. Here the tendency for the tie formation between two individuals due to the overlap in their features represents homophily. We find a phase transition as a function of F or q, resulting in a phase diagram. For fixed q and as a function of F the system shows two phases separated at Fc. For F < Fc large, homogeneous, and well separated communities can be identified within which the features match almost perfectly (segregated phase). When F becomes larger than Fc, the nodes start to belong to several communities and within a community the features match only partially (overlapping phase). Several quantities reflect this transition, including the average degree, clustering coefficient, feature overlap, and the number of communities per node. We also make an attempt to interpret these results in terms of observations on social behavior of humans.
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Affiliation(s)
- Yohsuke Murase
- RIKEN Center for Computational Science, Kobe, Hyogo, 650-0047, Japan.
| | - Hang-Hyun Jo
- Asia Pacific Center for Theoretical Physics, Pohang, 37673, Republic of Korea
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Republic of Korea
- Department of Computer Science, Aalto University, Espoo, FI-00076, Finland
| | - János Török
- Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, H-1111, Hungary
- Department of Network and Data Science, Central European University, Budapest, H-1051, Hungary
- MTA-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Budapest, H-1111, Hungary
| | - János Kertész
- Department of Computer Science, Aalto University, Espoo, FI-00076, Finland.
- Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, H-1111, Hungary.
- Department of Network and Data Science, Central European University, Budapest, H-1051, Hungary.
| | - Kimmo Kaski
- Department of Computer Science, Aalto University, Espoo, FI-00076, Finland
- The Alan Turing Institute, British Library, London, NW1 2DB, UK
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14
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Min B, San Miguel M. Competing contagion processes: Complex contagion triggered by simple contagion. Sci Rep 2018; 8:10422. [PMID: 29991815 PMCID: PMC6039514 DOI: 10.1038/s41598-018-28615-3] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Accepted: 06/26/2018] [Indexed: 11/08/2022] Open
Abstract
Empirical evidence reveals that contagion processes often occur with competition of simple and complex contagion, meaning that while some agents follow simple contagion, others follow complex contagion. Simple contagion refers to spreading processes induced by a single exposure to a contagious entity while complex contagion demands multiple exposures for transmission. Inspired by this observation, we propose a model of contagion dynamics with a transmission probability that initiates a process of complex contagion. With this probability nodes subject to simple contagion get adopted and trigger a process of complex contagion. We obtain a phase diagram in the parameter space of the transmission probability and the fraction of nodes subject to complex contagion. Our contagion model exhibits a rich variety of phase transitions such as continuous, discontinuous, and hybrid phase transitions, criticality, tricriticality, and double transitions. In particular, we find a double phase transition showing a continuous transition and a following discontinuous transition in the density of adopted nodes with respect to the transmission probability. We show that the double transition occurs with an intermediate phase in which nodes following simple contagion become adopted but nodes with complex contagion remain susceptible.
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Affiliation(s)
- Byungjoon Min
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain.
- Department of Physics, Chungbuk National University, Cheongju, Chungbuk, 28644, Korea.
| | - Maxi San Miguel
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain.
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15
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Peralta AF, Carro A, San Miguel M, Toral R. Analytical and numerical study of the non-linear noisy voter model on complex networks. CHAOS (WOODBURY, N.Y.) 2018; 28:075516. [PMID: 30070524 DOI: 10.1063/1.5030112] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Accepted: 06/22/2018] [Indexed: 06/08/2023]
Abstract
We study the noisy voter model using a specific non-linear dependence of the rates that takes into account collective interaction between individuals. The resulting model is solved exactly under the all-to-all coupling configuration and approximately in some random network environments. In the all-to-all setup, we find that the non-linear interactions induce bona fide phase transitions that, contrary to the linear version of the model, survive in the thermodynamic limit. The main effect of the complex network is to shift the transition lines and modify the finite-size dependence, a modification that can be captured with the introduction of an effective system size that decreases with the degree heterogeneity of the network. While a non-trivial finite-size dependence of the moments of the probability distribution is derived from our treatment, mean-field exponents are nevertheless obtained in the thermodynamic limit. These theoretical predictions are well confirmed by numerical simulations of the stochastic process.
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Affiliation(s)
- A F Peralta
- IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), Universitat de les Illes Balears-CSIC, 07122 Palma de Mallorca, Spain
| | - A Carro
- Institute for New Economic Thinking at the Oxford Martin School, University of Oxford, OX2 6ED Oxford, UK
| | - M San Miguel
- IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), Universitat de les Illes Balears-CSIC, 07122 Palma de Mallorca, Spain
| | - R Toral
- IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), Universitat de les Illes Balears-CSIC, 07122 Palma de Mallorca, Spain
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16
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Abstract
We introduce the threshold q-voter opinion dynamics where an agent, facing a binary choice, can change its mind when at least q_{0} among q neighbors share the opposite opinion. Otherwise, the agent can still change its mind with a certain probability ɛ. This threshold dynamics contemplates the possibility of persuasion by an influence group even when there is not full agreement among its members. In fact, individuals can follow their peers not only when there is unanimity (q_{0}=q) in the lobby group, as assumed in the q-voter model, but also, depending on the circumstances, when there is simple majority (q_{0}>q/2), Byzantine consensus (q_{0}>2q/3), or any minimal number q_{0} among q. This realistic threshold gives place to emerging collective states and phase transitions which are not observed in the standard q voter. The threshold q_{0}, together with the stochasticity introduced by ɛ, yields a phenomenology that mimics as particular cases the q voter with stochastic drivings such as nonconformity and independence. In particular, nonconsensus majority states are possible, as well as mixed phases. Continuous and discontinuous phase transitions can occur, but also transitions from fluctuating phases into absorbing states.
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Affiliation(s)
- Allan R Vieira
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil
| | - Celia Anteneodo
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil
- National Institute of Science and Technology for Complex Systems, Brazil
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