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Vilone D, Polizzi E. Modeling opinion misperception and the emergence of silence in online social system. PLoS One 2024; 19:e0296075. [PMID: 38206989 PMCID: PMC10783706 DOI: 10.1371/journal.pone.0296075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 12/05/2023] [Indexed: 01/13/2024] Open
Abstract
In the last decades an increasing deal of research has investigated the phenomenon of opinion misperception in human communities and, more recently, in social media. Opinion misperception is the wrong evaluation by community's members of the real distribution of opinions or beliefs about a given topic. In this work we explore the mechanisms giving rise to opinion misperception in social media groups, which are larger than physical ones and have peculiar topological features. By means of numerical simulations, we suggest that the structure of connections of such communities plays indeed a role in distorting the perception of the agents about others' beliefs, but it is essentially an indirect effect. Moreover, we show that the main ingredient that generates misperception is a spiral of silence induced by few, well connected and charismatic agents, which rapidly drives the majority of individuals to stay silent without disclosing their true belief, leading minoritarian opinions to appear more widespread throughout the community.
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Affiliation(s)
- Daniele Vilone
- LABSS (Laboratory of Agent Based Social Simulation), Institute of Cognitive Science and Technology, National Research Council (CNR), Rome, Italy
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain
| | - Eugenia Polizzi
- LABSS (Laboratory of Agent Based Social Simulation), Institute of Cognitive Science and Technology, National Research Council (CNR), Rome, Italy
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Li Q, Yu H, Han W, Wu Y. Group percolation in interdependent networks with reinforcement network layer. CHAOS (WOODBURY, N.Y.) 2022; 32:093126. [PMID: 36182370 DOI: 10.1063/5.0091342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
In many real-world interdependent network systems, nodes often work together to form groups, which can enhance robustness to resist risks. However, previous group percolation models are always of a first-order phase transition, regardless of the group size distribution. This motivates us to investigate a generalized model for group percolation in interdependent networks with a reinforcement network layer to eliminate collapse. Some backup devices that are equipped for a density ρ of reinforced nodes constitute the reinforcement network layer. For each group, we assume that at least one node of the group can function in one network and a node in another network depends on the group to function. We find that increasing the density ρ of reinforcement nodes and the size S of the dependency group can significantly enhance the robustness of interdependent networks. Importantly, we find the existence of a hybrid phase transition behavior and propose a method for calculating the shift point of percolation types. The most interesting finding is the exact universal solution to the minimal density ρ of reinforced nodes (or the minimum group size S) to prevent abrupt collapse for Erdős-Rényi, scale-free, and regular random interdependent networks. Furthermore, we present the validity of the analytic solutions for a triple point ρ (or S ), the corresponding phase transition point p , and second-order phase transition points p in interdependent networks. These findings might yield a broad perspective for designing more resilient interdependent infrastructure networks.
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Affiliation(s)
- Qian Li
- Institute of Information Technology, PLA Strategic Support Force, Information Engineering University, Zhengzhou 450000, China
| | - Hongtao Yu
- Institute of Information Technology, PLA Strategic Support Force, Information Engineering University, Zhengzhou 450000, China
| | - Weitao Han
- Institute of Information Technology, PLA Strategic Support Force, Information Engineering University, Zhengzhou 450000, China
| | - Yiteng Wu
- Institute of Information Technology, PLA Strategic Support Force, Information Engineering University, Zhengzhou 450000, China
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Qing T, Dong G, Wang F, Du R, Tian L. Phase transition behavior of finite clusters under localized attack. CHAOS (WOODBURY, N.Y.) 2022; 32:023105. [PMID: 35232027 DOI: 10.1063/5.0079489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Most previous studies focused on the giant component to explore the structural robustness of complex networks under malicious attacks. As an important failure mode, localized attacks (LA) can excellently describe the local failure diffusion mechanism of many real scenarios. However, the phase transition behavior of finite clusters, as important network components, has not been clearly understood yet under LA. Here, we develop a percolation framework to theoretically and simulatively study the phase transition behavior of functional nodes belonging to the finite clusters of size greater than or equal to s(s=2,3,…) under LA in this paper. The results reveal that random network exhibits second-order phase transition behavior, the critical threshold pc increases significantly with increasing s, and the network becomes vulnerable. In particular, we find a new general scaling relationship with the critical exponent δ=-2 between the fraction of finite clusters and s. Furthermore, we apply the theoretical framework to some real networks and predict the phase transition behavior of finite clusters in real networks after they face LA. The framework and results presented in this paper are helpful to promote the design of more critical infrastructures and inspire new insights into studying phase transition behaviors for finite clusters in the network.
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Affiliation(s)
- Ting Qing
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China
| | - Gaogao Dong
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China
| | - Fan Wang
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China
| | - Ruijin Du
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China
| | - Lixin Tian
- School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China
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Coloured random graphs explain the structure and dynamics of cross-linked polymer networks. Sci Rep 2020; 10:14627. [PMID: 32884043 PMCID: PMC7471966 DOI: 10.1038/s41598-020-71417-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2020] [Accepted: 08/13/2020] [Indexed: 11/09/2022] Open
Abstract
Step-growth and chain-growth are two major families of chemical reactions that result in polymer networks with drastically different physical properties, often referred to as hyper-branched and cross-linked networks. In contrast to step-growth polymerisation, chain-growth forms networks that are history-dependent. Such networks are defined not just by the degree distribution, but also by their entire formation history, which entails a modelling and conceptual challenges. We show that the structure of chain-growth polymer networks corresponds to an edge-coloured random graph with a defined multivariate degree distribution, where the colour labels represent the formation times of chemical bonds. The theory quantifies and explains the gelation in free-radical polymerisation of cross-linked polymers and predicts conditions when history dependance has the most significant effect on the global properties of a polymer network. As such, the edge colouring is identified as the key driver behind the difference in the physical properties of step-growth and chain-growth networks. We expect that this findings will stimulate usage of network science tools for discovery and design of cross-linked polymers.
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Bonneau H, Biham O, Kühn R, Katzav E. Statistical analysis of edges and bredges in configuration model networks. Phys Rev E 2020; 102:012314. [PMID: 32794990 DOI: 10.1103/physreve.102.012314] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2020] [Accepted: 07/06/2020] [Indexed: 11/07/2022]
Abstract
A bredge (bridge-edge) in a network is an edge whose deletion would split the network component on which it resides into two separate components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node or link failures, attacks, or epidemics. Therefore, the abundance and properties of bredges affect the resilience of the network to these collapse scenarios. We present analytical results for the statistical properties of bredges in configuration model networks. Using a generating function approach based on the cavity method, we calculate the probability P[over ̂](e∈B) that a random edge e in a configuration model network with degree distribution P(k) is a bredge (B). We also calculate the joint degree distribution P[over ̂](k,k^{'}|B) of the end-nodes i and i^{'} of a random bredge. We examine the distinct properties of bredges on the giant component (GC) and on the finite tree components (FC) of the network. On the finite components all the edges are bredges and there are no degree-degree correlations. We calculate the probability P[over ̂](e∈B|GC) that a random edge on the giant component is a bredge. We also calculate the joint degree distribution P[over ̂](k,k^{'}|B,GC) of the end-nodes of bredges and the joint degree distribution P[over ̂](k,k^{'}|NB,GC) of the end-nodes of nonbredge edges on the giant component. Surprisingly, it is found that the degrees k and k^{'} of the end-nodes of bredges are correlated, while the degrees of the end-nodes of nonbredge edges are uncorrelated. We thus conclude that all the degree-degree correlations on the giant component are concentrated on the bredges. We calculate the covariance Γ(B,GC) of the joint degree distribution of end-nodes of bredges and show it is negative, namely bredges tend to connect high degree nodes to low degree nodes. We apply this analysis to ensembles of configuration model networks with degree distributions that follow a Poisson distribution (Erdős-Rényi networks), an exponential distribution and a power-law distribution (scale-free networks). The implications of these results are discussed in the context of common attack scenarios and network dismantling processes.
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Affiliation(s)
- Haggai Bonneau
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
| | - Ofer Biham
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
| | - Reimer Kühn
- Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Eytan Katzav
- Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
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Kryven I, Ziff RM, Bianconi G. Renormalization group for link percolation on planar hyperbolic manifolds. Phys Rev E 2019; 100:022306. [PMID: 31574679 DOI: 10.1103/physreve.100.022306] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2019] [Indexed: 11/07/2022]
Abstract
Network geometry is currently a topic of growing scientific interest, as it opens the possibility to explore and interpret the interplay between structure and dynamics of complex networks using geometrical arguments. However, the field is still in its infancy. In this work we investigate the role of network geometry in determining the nature of the percolation transition in planar hyperbolic manifolds. Boettcher et al. [Nat. Comm. 3, 787 (2012)2041-172310.1038/ncomms1774] have shown that a special type of two-dimensional hyperbolic manifolds, the Farey graphs, display a discontinuous transition for ordinary link percolation. Here we investigate using the renormalization group the critical properties of link percolation on a wider class of two-dimensional hyperbolic deterministic and random manifolds constituting the skeletons of two-dimensional cell complexes. These hyperbolic manifolds are built iteratively by subsequently gluing m-polygons to single edges. We show that when the size m of the polygons is drawn from a distribution q_{m} with asymptotic power-law scaling q_{m}≃Cm^{-γ} for m≫1, different universality classes can be observed depending on the value of the power-law exponent γ. Interestingly, the percolation transition is hybrid for γ∈(3,4) and becomes continuous for γ∈(2,3].
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Affiliation(s)
- Ivan Kryven
- Mathematical Institute, Utrecht University, PO Box 80010, 3508 TA Utrecht, the Netherlands
| | - Robert M Ziff
- Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom and Alan Turing Institute, 96 Euston Rd, London, NW1 2DB, United Kingdom
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Schamboeck V, Iedema PD, Kryven I. Dynamic Networks that Drive the Process of Irreversible Step-Growth Polymerization. Sci Rep 2019; 9:2276. [PMID: 30783151 PMCID: PMC6381213 DOI: 10.1038/s41598-018-37942-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Accepted: 12/18/2018] [Indexed: 11/15/2022] Open
Abstract
Many research fields, reaching from social networks and epidemiology to biology and physics, have experienced great advance from recent developments in random graphs and network theory. In this paper we propose a generic model of step-growth polymerisation as a promising application of the percolation on a directed random graph. This polymerisation process is used to manufacture a broad range of polymeric materials, including: polyesters, polyurethanes, polyamides, and many others. We link features of step-growth polymerisation to the properties of the directed configuration model. In this way, we obtain new analytical expressions describing the polymeric microstructure and compare them to data from experiments and computer simulations. The molecular weight distribution is related to the sizes of connected components, gelation to the emergence of the giant component, and the molecular gyration radii to the Wiener index of these components. A model on this level of generality is instrumental in accelerating the design of new materials and optimizing their properties, as well as it provides a vital link between network science and experimentally observable physics of polymers.
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Affiliation(s)
- Verena Schamboeck
- University of Amsterdam, Van't Hoff Institute for Molecular Sciences, Amsterdam, 1090 GE, The Netherlands.
| | - Piet D Iedema
- University of Amsterdam, Van't Hoff Institute for Molecular Sciences, Amsterdam, 1090 GE, The Netherlands
| | - Ivan Kryven
- University of Amsterdam, Van't Hoff Institute for Molecular Sciences, Amsterdam, 1090 GE, The Netherlands
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Kryven I. Bond percolation in coloured and multiplex networks. Nat Commun 2019; 10:404. [PMID: 30679430 PMCID: PMC6345799 DOI: 10.1038/s41467-018-08009-9] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2018] [Accepted: 12/10/2018] [Indexed: 11/09/2022] Open
Abstract
Percolation in complex networks is a process that mimics network degradation and a tool that reveals peculiarities of the network structure. During the course of percolation, the emergent properties of networks undergo non-trivial transformations, which include a phase transition in the connectivity, and in some special cases, multiple phase transitions. Such global transformations are caused by only subtle changes in the degree distribution, which locally describe the network. Here we establish a generic analytic theory that describes how structure and sizes of all connected components in the network are affected by simple and colour-dependent bond percolations. This theory predicts locations of the phase transitions, existence of wide critical regimes that do not vanish in the thermodynamic limit, and a phenomenon of colour switching in small components. These results may be used to design percolation-like processes, optimise network response to percolation, and detect subtle signals preceding network collapse. Percolation is a tool used to investigate a network’s response as random links are removed. Here the author presents a generic analytic theory to describe how percolation properties are affected in coloured networks, where the colour can represent a network feature such as multiplexity or the belonging to a community.
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Affiliation(s)
- Ivan Kryven
- Van't Hoff Institute for Molecular Sciences, University of Amsterdam, PO Box 94157, 1090 GD, Amsterdam, The Netherlands.
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Torres-Knoop A, Kryven I, Schamboeck V, Iedema PD. Modeling the free-radical polymerization of hexanediol diacrylate (HDDA): a molecular dynamics and graph theory approach. SOFT MATTER 2018; 14:3404-3414. [PMID: 29667682 DOI: 10.1039/c8sm00451j] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In the printing, coating and ink industries, photocurable systems are becoming increasingly popular and multi-functional acrylates are one of the most commonly used monomers due to their high reactivity (fast curing). In this paper, we use molecular dynamics and graph theory tools to investigate the thermo-mechanical properties and topology of hexanediol diacrylate (HDDA) polymer networks. The gel point was determined as the point where a giant component was formed. For the conditions of our simulations, we found the gel point to be around 0.18 bond conversion. A detailed analysis of the network topology showed, unexpectedly, that the flexibility of the HDDA molecules plays an important role in increasing the conversion of double bonds, while delaying the gel point. This is due to a back-biting type of reaction mechanism that promotes the formation of small cycles. The glass transition temperature for several degrees of curing was obtained from the change in the thermal expansion coefficient. For a bond conversion close to experimental values we obtained a glass transition temperature around 400 K. For the same bond conversion we estimate a Young's modulus of 3 GPa. Both of these values are in good agreement with experiments.
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Affiliation(s)
- Ariana Torres-Knoop
- Van't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
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Kryven I. Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions. Phys Rev E 2018; 96:052304. [PMID: 29347790 DOI: 10.1103/physreve.96.052304] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2017] [Indexed: 11/07/2022]
Abstract
This work presents exact expressions for size distributions of weak and multilayer connected components in two generalizations of the configuration model: networks with directed edges and multiplex networks with an arbitrary number of layers. The expressions are computable in a polynomial time and, under some restrictions, are tractable from the asymptotic theory point of view. If first partial moments of the degree distribution are finite, the size distribution for two-layer connected components in multiplex networks exhibits an exponent -3/2 in the critical regime, whereas the size distribution of weakly connected components in directed networks exhibits two critical exponents -1/2 and -3/2.
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Affiliation(s)
- Ivan Kryven
- Van 't Hoff Institute for Molecular Sciences, University of Amsterdam, PO Box 94214, 1090 GE Amsterdam, Netherlands
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Schamboeck V, Kryven I, Iedema PD. Acrylate Network Formation by Free-Radical Polymerization Modeled Using Random Graphs. MACROMOL THEOR SIMUL 2017. [DOI: 10.1002/mats.201700047] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Verena Schamboeck
- Van't Hoff Institute for Molecular Sciences; University of Amsterdam; P.O. Box 94157 1090 GD Amsterdam The Netherlands
| | - Ivan Kryven
- Van't Hoff Institute for Molecular Sciences; University of Amsterdam; P.O. Box 94157 1090 GD Amsterdam The Netherlands
| | - Pieter D. Iedema
- Van't Hoff Institute for Molecular Sciences; University of Amsterdam; P.O. Box 94157 1090 GD Amsterdam The Netherlands
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