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In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degree-assortative network, that is to say a network where sites with similar degree are connected each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure.
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In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the nodes importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two nodes are connected, they tend to have similar node degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same. This is also true if we measure the average prominence of neighbours of the two people. This property is weaker or negative in non-social networks. We investigate a number of possible explanations for this property. However, none of them was found to provide an adequate explanation. We therefore conclude that second-order assortative mixing is a new property of social networks.
Inspired by the analysis of several empirical online social networks, we propose a simple reaction-diffusion-like coevolving model, in which individuals are activated to create links based on their states, influenced by local dynamics and their own intention. It is shown that the model can reproduce the remarkable properties observed in empirical online social networks; in particular, the assortative coefficients are neutral or negative, and the power law exponents are smaller than 2. Moreover, we demonstrate that, under appropriate conditions, the model network naturally makes transition(s) from assortative to disassortative, and from sparse to dense in their characteristics. The model is useful in understanding the formation and evolution of online social networks.
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend to connect to other highly connected vertices, and have broad degree distributions. We present a model for an undirected growing network which reproduces these characteristics, with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena. The communities arise from a mixture of random attachment and implicit preferential attachment. The structural properties of the model are studied analytically and numerically, using the $k$-clique method for quantifying the communities.
On-line social networks, such as in Facebook and Twitter, are often studied from the perspective of friendship ties between agents in the network. Adversarial ties, however, also play an important role in the structure and function of social networks, but are often hidden. Underlying generative mechanisms of social networks are predicted by structural balance theory, which postulates that triads of agents, prefer to be transitive, where friends of friends are more likely friends, or anti-transitive, where adversaries of adversaries become friends. The previously proposed Iterated Local Transitivity (ILT) and Iterated Local Anti-Transitivity (ILAT) models incorporated transitivity and anti-transitivity, respectively, as evolutionary mechanisms. These models resulted in graphs with many observable properties of social networks, such as low diameter, high clustering, and densification. We propose a new, generative model, referred to as the Iterated Local Model (ILM) for social networks synthesizing both transitive and anti-transitive triads over time. In ILM, we are given a countably infinite binary sequence as input, and that sequence determines whether we apply a transitive or an anti-transitive step. The resulting model exhibits many properties of complex networks observed in the ILT and ILAT models. In particular, for any input binary sequence, we show that asymptotically the model generates finite graphs that densify, have clustering coefficient bounded away from 0, have diameter at most 3, and exhibit bad spectral expansion. We also give a thorough analysis of the chromatic number, domination number, Hamiltonicity, and isomorphism types of induced subgraphs of ILM graphs.
In this big data era, more and more social activities are digitized thereby becoming traceable, and thus the studies of social networks attract increasing attention from academia. It is widely believed that social networks play important role in the process of information diffusion. However, the opposite question, i.e., how does information diffusion process rebuild social networks, has been largely ignored. In this paper, we propose a new framework for understanding this reversing effect. Specifically, we first introduce a novel information diffusion model on social networks, by considering two types of individuals, i.e., smart and normal individuals, and two kinds of messages, true and false messages. Since social networks consist of human individuals, who have self-learning ability, in such a way that the trust of an individual to one of its neighbors increases (or decreases) if this individual received a true (or false) message from that neighbor. Based on such a simple self-learning mechanism, we prove that a social network can indeed become smarter, in terms of better distinguishing the true message from the false one. Moreover, we observe the emergence of social stratification based on the new model, i.e., the true messages initially posted by an individual closer to the smart one can be forwarded by more others, which is enhanced by the self-learning mechanism. We also find the crossover advantage, i.e., interconnection between two chain networks can make the related individuals possessing higher social influences, i.e., their messages can be forwarded by relatively more others. We obtained these results theoretically and validated them by simulations, which help better understand the reciprocity between social networks and information diffusion.
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