Exploring the rich-club characteristic in internal migration: Evidence from Chinese Chunyun migration
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Internal migration
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Nodes distribution by degrees is the most important characteristic of complex networks, but not comprehensive one. While degree distribution is a first order graph metric, the assortativity is a second order one. Assortativity coefficient is a measure of a tendency for nodes in networks to connect with similar or dissimilar ones in some way. As a simplest case, assortative mixing is considered according to nodes degree. In general, degree distribution forms an essential restriction both on the network structure and on assortativity coefficient boundaries. The problem of determining the structure of SF- networks having an extreme assortativity coefficient is considered. The estimates of boundaries for assortativity coefficient have been found. It was found, that these boundaries are as wider as scaling factor of SF-model is far from one of BA-model. In addition, the boundaries are narrowing with increasing the network size.
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Assortativity has been widely studied for understanding the structure and function of complex networks. Assortative is defined as an association of items with other items having similar characteristics. The research has shown that assortativity has a significant impact on many processes on networks, including information cascades, spreading, congestion relief, longevity, and epidemic thresholds. The degree distribution is also an important factor that affects some of these results. In this paper, we introduce a simple but effective method for adjusting a given network while preserving the degree distribution of the network and, if desired, the connectivity of the network. The algorithm is tested on both theoretical and real-world networks and is supported by detailed empirical results. We illustrate how changing assortativity affects some network properties. The method can be useful for researchers interested in the relationship of assortativity to network structures and the dynamics of processes on networks.
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Assortativity
Degree distribution
Mixing patterns
Degree (music)
Social network (sociolinguistics)
Evolutionary Dynamics
Dynamic network analysis
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Assortativity
Social network (sociolinguistics)
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Assortativity
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Assortativity quantifies the tendency of nodes being connected to similar nodes in a complex network. Degree Assortativity can be quantified as a Pearson correlation. However, it is insufficient to explain assortative or disassortative tendencies of individual nodes or links, which may be contrary to the overall tendency of the network. A number of 'local' assortativity measures have been proposed to address this. In this paper we define and analyse an alternative formulation for node assortativity, primarily for undirected networks. The alternative approach is justified by some inherent shortcomings of existing local measures of assortativity. Using this approach, we show that most real world scale-free networks have disassortative hubs, though we can synthesise model networks which have assortative hubs. Highlighting the relationship between assortativity of the hubs and network robustness, we show that real world networks do display assortative hubs in some instances, particularly when high robustness to targeted attacks is a necessity.
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We survey the concept of assortativity, starting from its original definition by Newman in 2002. Degree assortativity is the most commonly used form of assortativity. Degree assortativity is extensively used in network science. Since degree assortativity alone is not sufficient as a graph analysis tool, assortativity is usually combined with other graph metrics. Much of the research on assortativity considers undirected, non-weighted networks. The research on assortativity needs to be extended to encompass also directed links and weighted links. In addition, the relation between assortativity and line graphs, complementary graphs and graph spectra needs further work, to incorporate directed graphs and weighted links. The present survey paper aims to summarize the work in this area and provides a new scope of research.
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Assortativity
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Social forces connect individuals in different ways. When individuals get connected, one can observe distinguishable patterns in their connectivity networks. One such pattern is assortativity, also known as social similarity. In networks with assortativity, similar nodes are connected to one another more often than dissimilar nodes. For instance, in social networks, a high similarity between friends is observed. This similarity is exhibited by similar behavior, similar interests, similar activities, and shared attributes such as language, among others. In other words, friendship networks are assortative. Investigating assortativity patterns that individuals exhibit on social media helps one better understand user interactions. Assortativity is the most commonly observed pattern among linked individuals. This chapter discusses assortativity along with principal factors that result in assortative networks.
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