Universal evolution patterns of degree assortativity in social networks
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Assortativity
Degree distribution
Mixing patterns
Degree (music)
Social network (sociolinguistics)
Evolutionary Dynamics
Dynamic network analysis
Due to the recent availability of large complex networks, considerable analysis has focused on understanding and characterizing the properties of these networks. Scalable generative graph models focus on modeling distributions of graphs that match real world network properties and scale to large datasets. Much work has focused on modeling networks with a power law degree distribution, clustering, and small diameter. In network analysis, the assortativity statistic is defined as the correlation between the degrees of linked nodes in the network. The assortativity measure can distinguish between types of networks---social networks commonly exhibit positive assortativity, in contrast to biological or technological networks that are typically disassortative. Despite this, little work has focused on scalable graph models that capture assortativity in networks. The contributions of our work are twofold. First, we prove that an unbounded number of pairs of networks exist with the same degree distribution and assortativity, yet different joint degree distributions. Thus, assortativity as a network measure cannot distinguish between graphs with complex (non-linear) dependence in their joint degree distributions. Motivated by this finding, we introduce a generative graph model that explicitly estimates and models the joint degree distribution. Our Binned Chung Lu method accurately captures both the joint degree distribution and assortativity, while still matching characteristics such as the degree distribution and clustering coefficients. Further, our method has subquadratic learning and sampling methods that enable scaling to large, real world networks. We evaluate performance compared to other scalable graph models on six real world networks, including a citation network with over 14 million edges.
Assortativity
Degree distribution
Clustering coefficient
Degree (music)
Generative model
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Assortativity
Degree distribution
Degree (music)
Scale-free network
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Assortativity
Degree distribution
Mixing patterns
Degree (music)
Social network (sociolinguistics)
Evolutionary Dynamics
Dynamic network analysis
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Citations (18)
We focus on spatially-extended networks during their transition from short-range connectivities to a scale-free structure expressed by heavy-tailed degree-distribution. In particular, a model is introduced for the generation of such graphs, which combines spatial growth and preferential attachment. In this model the transition to heterogeneous structures is always accompanied by a change in the graph's degree-degree correlation properties: while high assortativity levels characterize the dominance of short distance couplings, long-range connectivity structures are associated with small amounts of disassortativity. Our results allow to infer that a disassortative mixing is essential for establishing long-range links. We discuss also how our findings are consistent with recent experimental studies of 2-dimensional neuronal cultures.
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Degree distribution
Mixing patterns
Degree (music)
Preferential attachment
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Assortativity
Degree distribution
Clustering coefficient
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Assortativity
Clustering coefficient
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Small-world network
Scale-free network
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Abstract In sub-Sahara African countries the proportion of the population using Twitter (now known as X) and other social media networks is growing. Understanding these networks allows us to understand changes in how people interact with each other, share information and carry out economic transactions. We hypothesise that the networks of sub-Sahara African Twitter networks have statistical properties consistent with being built on a principle of self-organisation: where decisions about who to connect to are less influenced by large commercial actors (as they might be in Europe, USA and other parts of the world) and are instead on the basis of local interactions between individuals. To test this hypothesis, we first collected data on the Twitter network of users in Tanzania. We found that the degree distribution followed a power-law with degree close to 2. We calculated path lengths, clustering, and assortativity of mixing for this network, as well as identifying the most influential users using eigenvector centrality. We then tested the degree to which these measurements were consistent with a variation of a friend-of-a-friend model of network attachments: where links are formed by individuals who join a network first identifying one individual at random (a friend) and attach to them and then choose n q people who the initial individual follows and attach to each of them with probability q . We found that for q = 1 and n q = 40 the model reproduces many aspects of the Tanzanian network, including the degree and clustering distribution. This model is not consistent with, for example, the USA or Japanese Twitter networks. Taken together, the model and its comparison to data from different real world network, supports the self-organisation hypothesis: a rule under which new members of the network connect to a random person and 40 people they follow reproduces many aspects of how the Tanzanian Twitter network has grown.
Assortativity
Degree distribution
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Social network (sociolinguistics)
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Degree (music)
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A primary model of schoolmates and friends network is built in this paper based on social network services,topological structure of this network is studied combined with the knowledge of complex network theory. The actual relational data were obtained from an online social networking site-Renren.com open to college student,and network of schoolmates and friends was constructed upon the database.The statistical quantities such as degree distribution,average shortest path length,clustering coefficient,assortativity coefficient etc. are calculated and analyzed to capture the feature of the network. It is observed that the network is scale-free,has small-world property,and exhibits disassortative mixing pattern. Mechanism for the formation of some characteristics is also analyzed and primarily illustrated,providing empirical foundation for further research about dynamical behaviors.
Assortativity
Clustering coefficient
Average path length
Degree distribution
Social network (sociolinguistics)
Network Formation
Scale-free network
Mixing patterns
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The conventional wisdom is that social networks exhibit an assortative mixing pattern, whereas biological and technological networks show a disassortative mixing pattern. However, the recent research on the online social networks modifies the widespread belief, and many online social networks show a disassortative or neutral mixing feature. Especially, we found that an online social network, Wealink, underwent a transition from degree assortativity characteristic of real social networks to degree disassortativity characteristic of many online social networks, and the transition can be reasonably elucidated by a simple network model that we propose. The relations among network assortativity, clustering, and modularity are also discussed in the paper.
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Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used for the prediction of viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks and recent attempts have been made to use assortativity to address this shortcoming. In this paper, we show that adding assortativity does not fully explain the variance in the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution in combination with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data-driven approach by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95% of the variance in virality on networks with the same degree distribution but different network topologies. Our results not only highlight the importance of graphlets but also identify a small collection of graphlets which may have the highest influence over the viral processes on a network.
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