Assortative mixing
Encyclopedia
In the study of complex network
Complex network
In the context of network theory, a complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in real graphs...

s, assortative mixing, or assortativity
Assortativity
Assortativity is a preference for a network's nodes to attach to others that are similar or different in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's degree...

, is a bias in favor of connections between network nodes with similar characteristics. In the specific case of social networks, assortative mixing is also known as homophily
Homophily
Homophily is the tendency of individuals to associate and bond with similar others. The presence of homophily has been discovered in a vast array of network studies. Within their extensive review paper, sociologists McPherson, Smith-Lovin and Cook cite over one hundred studies that have observed...

. The rarer disassortative mixing is a bias in favor of connections between dissimilar nodes.

In social networks, for example, individuals commonly choose to associate with others of similar age, nationality, location, race, income, educational level, religion, or language as themselves. In networks of sexual contact
Sexual network
A sexual network is a social network that is defined by the sexual relationships within a set of individuals.-Studies and discoveries:Like other forms of social networks, sexual networks can be formally studied using the mathematics of graph theory and network theory.Recent epidemiological studies ...

, the same biases are observed, but mixing is also disassortative by gender – most partnerships are between individuals of opposite sex.

Assortative mixing can have effects, for example, on the spread of disease: if individuals have contact primarily with other members of the same population groups, then diseases will spread primarily within those groups. Many diseases are indeed known to have differing prevalence in different population groups, although other social and behavioral factors affect disease prevalence as well, including variations in quality of health care and differing social norms.

Assortative mixing is also observed in other (non-social) types of networks, including biochemical networks
Protein-protein interaction
Protein–protein interactions occur when two or more proteins bind together, often to carry out their biological function. Many of the most important molecular processes in the cell such as DNA replication are carried out by large molecular machines that are built from a large number of protein...

 in the cell, computer
Computer network
A computer network, often simply referred to as a network, is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information....

 and information
World Wide Web
The World Wide Web is a system of interlinked hypertext documents accessed via the Internet...

 networks, and others.

Of particular interest is the phenomenon of assortative mixing by degree
Degree (graph theory)
In graph theory, the degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice. The degree of a vertex v is denoted \deg. The maximum degree of a graph G, denoted by Δ, and the minimum degree of a graph, denoted by δ, are the maximum and minimum degree...

, meaning the tendency of nodes with high degree to connect to others with high degree, and similarly for low degree. Because degree is itself a topological property of networks, this type of assortative mixing gives rise to more complex structural effects than other types. Empirically it has been observed that most social networks mix assortatively by degree, but most networks of other types mix disassortatively, although there are exceptions.

See also

  • Assortativity
    Assortativity
    Assortativity is a preference for a network's nodes to attach to others that are similar or different in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's degree...

  • Complex network
    Complex network
    In the context of network theory, a complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in real graphs...

  • Graph theory
    Graph theory
    In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

  • Friendship paradox
    Friendship paradox
    The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. It can be explained as a form of sampling bias in which people with greater numbers of friends have an increased likelihood of...

  • Homophily
    Homophily
    Homophily is the tendency of individuals to associate and bond with similar others. The presence of homophily has been discovered in a vast array of network studies. Within their extensive review paper, sociologists McPherson, Smith-Lovin and Cook cite over one hundred studies that have observed...

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