Scale-free Social Networks Research Articles

The coupled dynamics of information-behavior-epidemic propagation considering the heterogeneity of adoption thresholds and network structures in multiplex networks

During epidemics, individual responses to prevention and control information vary significantly, affecting the execution of preventive measures. This paper introduces a novel model to analyze the co-evolution of the information-behavior-epidemic dynamic, accounting for the heterogeneity in individual behavioral adoption thresholds and network structures. The model consists of three layers: the upper layer, utilizing scale-free social networks to represent the diffusion of information; the middle and lower layers, employing community networks, to illustrate individuals’ decision-making and epidemic transmission processes, respectively. We applied the Heaviside step function to depict the effects of information and local environmental factors on individuals’ decisions. Through the microscopic Markov chain approach (MMCA), we determined the epidemic threshold. Our methodology also included extensive Monte Carlo (MC) simulations to validate our theoretical predictions. Our results reveal several key insights: (i) reducing community mobility and the threshold for adopting preventive behaviors can significantly restrain the scale of the epidemic and delay outbreaks; (ii) the level of individual activity in the physical contact network has a significant influence on epidemic transmission; (iii) integrating individuals’ behavior adoption thresholds induces a two-stage phase change, deviating from the continuous phase transition typically observed in epidemic transmission.

Effect of Segregation on Opinion Formation in Scale-Free Social Networks: An Agent-based Approach

We consider the effect of segregation on opinion formation in social networks with and without influential leaders in scale-free random networks, which is found in many social and natural phenomena. We have used agent-based modeling and simulation, focusing on the social impact model of opinion formation. Two simulation scenarios of this opinion formation model have been considered: (1) the original scenario which randomly assigns persuasion strengths to the agents, and (2) a centrality-based scenario, which assigns persuasion strengths proportional to the agents’ centralities. In the latter scenario, hubs are considered more influential leaders who are more connected to others and have higher persuasion strengths than others. The simulation results show a correlation between segregation and change of population opinion in the original model, but no correlation between both variables in the centrality-based scenario. The results lead us to conclude that with strong influential leaders in society, the effect of segregation in opinion formation is neglectable.

De-anonymizing Scale-Free Social Networks by Using Spectrum Partitioning Method

Social network data is widely shared, forwarded and published to third parties, which led to the risks of privacy disclosure. Even thought the network provider always perturbs the data before publishing it, attackers can still recover anonymous data according to the collected auxiliary information. In this paper, we transform the problem of de-anonymization into node matching problem in graph, and the de-anonymization method can reduce the number of nodes to be matched at each time. In addition, we use spectrum partitioning method to divide the social graph into disjoint subgraphs, and it can effectively be applied to large-scale social networks and executed in parallel by using multiple processors. Through the analysis of the influence of power-law distribution on de-anonymization, we synthetically consider the structural and personal information of users which made the feature information of the user more practical.

Online Social Networks (OSN) Evolution Model Based on Homophily and Preferential Attachment

In this paper, we propose a new scale-free social networks (SNs) evolution model that is based on homophily combined with preferential attachments. Our model enables the SN researchers to generate SN synthetic data for the evaluation of multi-facet SN models that are dependent on users’ attributes and similarities. Homophily is one of the key factors for interactive relationship formation in SN. The synthetic graph generated by our model is scale-invariant and has symmetric relationships. The model is dynamic and sustainable to changes in input parameters, such as number of nodes and nodes’ attributes, by conserving its structural properties. Simulation and evaluation of models for large-scale SN applications need large datasets. One way to get SN data is to generate synthetic data by using SN evolution models. Various SN evolution models are proposed to approximate the real-life SN graphs in previous research. These models are based on SN structural properties such as preferential attachment. The data generated by these models is suitable to evaluate SN models that are structure dependent but not suitable to evaluate models which depend on the SN users’ attributes and similarities. In our proposed model, users’ attributes and similarities are utilized to synthesize SN graphs. We evaluated the resultant synthetic graph by analyzing its structural properties. In addition, we validated our model by comparing its measures with the publicly available real-life SN datasets and previous SN evolution models. Simulation results show our resultant graph to be a close representation of real-life SN graphs with users’ attributes.

Tolerance analysis in scale-free social networks with varying degree exponents

PurposeThere are many complex networks like World-Wide Web, internet and social networks have been reported to be scale-free. The major property of scale-free networks is their degree distributions are in power law form. Generally, the degree exponents of scale-free networks fall into the range of (2, 3). The purpose of this paper is to investigate other situations where the degree exponents may lie outside the range.Design/methodology/approachIn this paper, analysis has been carried out by varying the degree exponents in the range of (0.5, 4.5). In total, 243 scenarios have been generated with varying network size of 1,000, 2,000 and 4,000, and degree exponents in the range of (0.5, 4.5) using interval of 0.05.FindingsThe following five indicators have been investigated: average density, average clustering coefficient, average path length, average diameter and average node degree. These indicators vary with the network size and degree exponent. If certain indicators do not satisfy with the user requirement using degree exponents of (2, 3), one can further increase or decrease the value with tradeoff. Results recommend that for degree exponents in (0.5, 2), 26 possible scale-free networks can be selected whereas for (3, 4.5), 41 possible scale-free networks can be selected, assuming a 100 percent deviation on the network parameters.Originality/valueA tolerance analysis is given for the tradeoff and guideline is drawn to help better design of scale-free network for degree exponents in range of (0.5, 2) and (3, 4.5) using network size 1,000, 2,000 and 4,000. The methodology is applicable to any network size.

Spatial utilization predicts animal social contact networks are not scale-free.

While heterogeneity in social behaviour has been described in many human contexts it is often assumed to be less common in the animal kingdom even though scale-free networks are observed. This homogeneity raises the question of whether the patterns of behaviour necessary to account for scale-free social contact networks, where the degree distribution follows a power law, i.e. a few individuals are very highly connected but most have only a few connections, occur in animals, or whether other mechanisms are needed to produce realistic contact network architectures. We develop a space-utilization model for individual animal behaviour to predict the individuals' social contact network. Using basic properties of the χ2 distribution we present a simple analytical result that allows the model to give a range of predictions with minimal computational effort. The model results are tested on data collected in New Zealand for the social contact networks of the wild brushtail possum (Trichosurus vulpecula). Our model provides a better prediction of network architecture than other simple models, including a scale-free model.

A novel performance measure for characterising efficient immunisation strategies in computer networks and populations

In this paper, an efficient immunisation strategy is devised for different types of networks, ranging from peer-to-peer computer networks to scale-free and small-world social networks. This strategy, named I-ring (I-chain), is proposed in order to immunise the random acquaintance between the independent nodes. As long as the data flow is not halted by failures, they are routed minimally through the network. However, if the information flow is blocked by failures, the routing restrictions may be relaxed by rerouting the message flow such that it bypasses the failed nodes and faulty region. The proposed strategy requires no knowledge of node degrees or general information about the network and its topology. Most importantly, a novel performance measure is evolved to assess the reliability and robustness of networks, that is the probability of messages facing the I-ring (I-chain). The experimental results of simulations testify the accuracy and practicability of the proposed measure.

Ivga: A fast force-directed method for interactive visualization of complex networks

Complex networks play a very important role in various fields of science as data structures, which aggregate information about mutual relationships between numerous objects. The structural properties of these large graphs can be scrutinized throughout their interactive visualization. However, visual analysis of complex networks consisting of |V|∼106+ vertices represents a great challenge for nowadays computer systems both from computational and storage perspective. Therefore, the existing graph drawing methods involving greater than O(|V|) time and space complexity cannot be regarded as promising tools in the advent of the Big Data era. We present here a new and very fast graph drawing method with O(|V|) time and space complexity – ivga (interactive visualization of graphs). We evaluate its usefulness and performance by testing ivga on the large complex networks from the Stanford Large Network Dataset Collection. We demonstrate that ivga allows for very fast interactive visualization of large graphs consisting of up to a few million vertices on a regular laptop what makes it very competitive to other state-of-art graph drawing methods. Particularly, we recommend ivga method for interactive visualization of large non-planar complex networks such as small-world and scale-free social networks. The main concept of ivga can be seriously considered in developing tools for visualization and analysis of really huge networks, with billions of vertices and edges, on Big Data systems.

Coupling entropy of co-processing model on social networks

Coupling entropy of co-processing model on social networks is investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation. In order to understand the evolution of the co-processing and design the optimal routing strategy according to the maximal entropic diffusion on networks, we propose the coupling entropy comprehending the structural characteristics and information propagation on social network. Based on the analysis of the co-processing model, we analyze the coupling impact of the structural factor and information propagating factor on the coupling entropy, where the analytical results fit well with the numerical ones on scale-free social networks.

Dynamics of competing ideas in complex social systems

Individuals accepting an idea may intentionally or unintentionally impose influences in a certain neighborhood area, making it less likely or even impossible for other individuals within the area to accept competing ideas. Depending on whether such influences strictly prohibit neighborhood individuals from accepting other ideas or not, we classify them into exclusive and non-exclusive influences, respectively. Our study reveals, for the first time, the rich and complex dynamics of two competing ideas with neighborhood influences in scale-free social networks: depending on whether they have exclusive or non-exclusive influences, the final state varies from multiple co-existence to founder control to exclusion, with different sizes of population accepting each of the ideas, respectively. Such results provide helpful insights for better understanding of the spread (and the control of the spread) of ideas in human society.

Impact of social neighborhood on diffusion of innovation S-curve

Agent-based modeling (ABM) of Diffusion of Innovation (DOI) allows capturing of complex system phenomena that are related to social network topology, in contrast to traditional approaches such as Fisher-Pry or Bass models. These effects can be crucial for accurate prediction of DOI in the markets with strong influence of word-of-mouth. In this paper we compared DOI through random and scale-free social networks using ABM. The model predicts faster product adoption for a random network compared with a scale-free network with the same number of nodes due to the presence of hubs. Longer diffusion time in scale-free networks is related to lower information equality. Real world social networks can be a mixture of the two considered extreme cases and also can depend on the type of product.

Emergent Scale-free Social Networks in History: Burning and the Rise of English Protestantism

Abstract There is a large and rapidly increasing literature which analyses social networks for which substantial amounts of quantitative data are available. Further, there is a growing and related literature on what is referred to by economists as ‘information cascades’ on such networks. However, there is little discussion of the specific events which lead to either the creation of a network in the first instance, or of how a network which is latent in terms of its awareness evolves into a network on which individual behaviour/beliefs are actually altered. In this paper, we describe the process of emergence and evolution of a historical cultural and social network across which the opinions and behaviour of individuals were influenced. We also illustrate how empirical networks can be reconstructed relying principally on information contained in qualitative, historical sources. The specific example we use is religious belief in England in the 1550s. We describe how the burnings of Protestant leaders by the Catholic Queen Mary (1553-1558) created a set of martyrs which was decisive in increasing support not just for Protestantism compared to Catholicism, but which led to the rapid disappearance of rival Protestant factions. The network of awareness of key religious leaders already existed prior to Mary’s accession to the throne. But her actions converted this into a network on which individual beliefs were affected, in this case decisively for English history.

Theory of rumour spreading in complex social networks

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.