Statistical physics of social dynamics

Castellano, Claudio; Fortunato, Santo; Loreto, Vittorio

doi:10.1103/revmodphys.81.591

Cited by 3,500 publications

(3,764 citation statements)

References 491 publications

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“…One of these areas is sociophysics that studies how assumptions about the behavior and social interactions of people in a "microcospic level" creates emerging social behaviors, like opinion propagation, consensus formation, properties of elections, how wealth is distributed in society, among other topics. Typical approaches include modeling using deterministic cellular automata, Monte Carlo simulations of models derived from ferromagnetic models (usually Ising and Potts), mean-field approaches and diffusion-reaction processes [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Connections between the Sznajd model with general confidence rules and graph theory

Timpanaro

Prado

2012

Phys. Rev. E

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The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

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Section: Introductionmentioning

confidence: 99%

Connections between the Sznajd model with general confidence rules and graph theory

Timpanaro

Prado

2012

Phys. Rev. E

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“…Neutral diffusion-like or copying process models have been applied in a very broad range of fields, from social phenomena [1] and language change [2,3], to ecology [4,5,6] and population genetics [7] among many more. In all such models, different alternative items -species, opinions or language variants for example -are copied between neighbouring sites until one finally dominates the whole system.…”

Section: Introductionmentioning

confidence: 99%

A voter model with time dependent flip rates

Baxter¹

2011

J. Stat. Mech.

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Abstract. We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime. and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.

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“…These models have been used to describe disease spreading as well as information and rumour spreading in social processes where an actor constantly needs to be reminded 19 . We denote the probability that an infectious node will infect a susceptible neighbour as β.…”

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Identification of influential spreaders in complex networks

et al. 2010

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Networks portray a multitude of interactions through which people meet, ideas are spread and infectious diseases propagate within a society 1-5 . Identifying the most efficient 'spreaders' in a network is an important step towards optimizing the use of available resources and ensuring the more efficient spread of information. Here we show that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the most highly connected or the most central people 6-10 . Instead, we find that the most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis [11][12][13] , and that when multiple spreaders are considered simultaneously the distance between them becomes the crucial parameter that determines the extent of the spreading. Furthermore, we show that infections persist in the high-k shells of the network in the case where recovered individuals do not develop immunity. Our analysis should provide a route for an optimal design of efficient dissemination strategies.Spreading is a ubiquitous process, which describes many important activities in society [2][3][4][5] . The knowledge of the spreading pathways through the network of social interactions is crucial for developing efficient methods to either hinder spreading in the case of diseases, or accelerate spreading in the case of information dissemination. Indeed, people are connected according to the way they interact with one another in society and the large heterogeneity of the resulting network greatly determines the efficiency and speed of spreading. In the case of networks with a broad degree distribution (number of links per node) 6 , it is believed that the most connected people (hubs) are the key players, being responsible for the largest scale of the spreading process [6][7][8] . Furthermore, in the context of social network theory, the importance of a node for spreading is often associated with the betweenness centrality, a measure of how many shortest paths cross through this node, which is believed to determine who has more 'interpersonal influence' on others 9,10 .Here we argue that the topology of the network organization plays an important role such that there are plausible circumstances under which the highly connected nodes or the highest-betweenness nodes have little effect on the range of a given spreading process. For example, if a hub exists at the end of a branch at the periphery of a network, it will have a minimal impact in the spreading process through the core of the network, whereas a less connected person who is strategically placed in the core of the network will have a significant effect that leads to dissemination through a large fraction of the population. To identify the core and the periphery of the network we use the k-shell (also called k-core) decomposition of the network [11][12][13][14] . Examining this quantity in a number of real networks enables us to identify the best individual spreaders in the network when th...

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Statistical physics of social dynamics

Cited by 3,500 publications

References 491 publications

Connections between the Sznajd model with general confidence rules and graph theory

Connections between the Sznajd model with general confidence rules and graph theory

A voter model with time dependent flip rates

Identification of influential spreaders in complex networks

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