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Assortativity
Assortativity, or assortative mixing is a preference for a network's nodes to attach to others that are similar in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's degree. The addition of this characteristic to network models more closely approximates the behaviors of many real world networks. Correlations between nodes of similar degree are often found in the mixing patterns of many observable networks. For instance, in social networks, nodes tend to be connected with other nodes with similar degree values. This tendency is referred to as assortative mixing, or ''assortativity''. On the other hand, technological and biological networks typically show disassortative mixing, or ''disassortativity'', as high degree nodes tend to attach to low degree nodes. Measurement Assortativity is often operationalized as a correlation between two nodes. However, there are several ways to capture such a correlat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rich-club Coefficient
The rich-club coefficient is a metric on graphs and networks, designed to measure the extent to which well-connected nodes also connect to each other. Networks which have a relatively high rich-club coefficient are said to demonstrate the rich-club effect and will have many connections between nodes of high degree. The rich-club coefficient was first introduced in 2004 in a paper studying Internet topology.Mattia Gasparini, Javier Luis Canovas Izquierdo, Robert Clariso, Marco Brambilla, Jordi Cabot''Analyzing Rich-Club Behavior in Open Source Projects'' OpenSym 2019 proceedings The "Rich-club" effect has been measured and noted on scientific collaboration networks and air transportation networks. It has been shown to be significantly lacking on protein interaction networks. Definition Non-normalized form The rich-club coefficient was first introduced as an unscaled metric parametrized by node degree ranks. More recently, this has been updated to be parameterized in terms o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixing Patterns
Mixing patterns refer to systematic tendencies of one type of nodes in a network to connect to another type. For instance, nodes might tend to link to others that are very similar or very different. This feature is common in many social networks, although it also appears sometimes in non-social networks. Mixing patterns are closely related to assortativity; however, for the purposes of this article, the term is used to refer to assortative or disassortative mixing based on real-world factors, either topological or sociological. Types of Mixing Patterns Mixing patterns are a characteristic of an entire network, referring to the extent for nodes to connect to other similar or different nodes. Mixing, therefore, can be classified broadly as assortative or disassortative. ''Assortative mixing'' is the tendency for nodes to connect to like nodes, while ''disassortative mixing'' captures the opposite case in which very different nodes are connected. Obviously, the particular node charac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Cut-off
The structural cut-off is a concept in network science which imposes a degree cut-off in the degree distribution of a finite size network due to structural limitations (such as the simple graph property). Networks with vertices with degree higher than the structural cut-off will display structural disassortativity. Definition The structural cut-off is a maximum degree cut-off that arises from the structure of a finite size network. Let E_ be the number of edges between all vertices of degree k and k' if k \neq k', and twice the number if k=k'. Given that multiple edges between two vertices are not allowed, E_ is bounded by the maximum number of edges between two degree classes m_ . Then, the ratio can be written : r_ \equiv \frac = \frac , where \langle k \rangle is the average degree of the network, N is the total number of vertices, P(k) is the probability a randomly chosen vertex will have degree k, and P(k,k') = E_/\langle k \rangle N is the probability that a randomly p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assortative Mixing
In the study of complex networks, assortative mixing, or assortativity, 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. 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, 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 di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assortative Mixing
In the study of complex networks, assortative mixing, or assortativity, 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. 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, 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 di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Graph
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of ''typical'' graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, ''random graph'' refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a ''random graph''. Models A random graph is obtained by starting with a set of ''n'' isolated vertices and adding successive edges between them at random. The aim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homophily
Homophily () is a concept in sociology describing the tendency of individuals to associate and bond with similar others, as in the proverb "". The presence of homophily has been discovered in a vast array of network studies: over have observed homophily in some form or another, and they establish that similarity is associated with connection. The categories on which homophily occurs include age, gender, class, and organizational role. The opposite of homophily is heterophily or intermingling. Individuals in homophilic relationships share common characteristics (beliefs, values, education, etc.) that make communication and relationship formation easier. Homophily between mated pairs in animals has been extensively studied in the field of evolutionary biology, where it is known as ''assortative mating''. Homophily between mated pairs is common within natural animal mating populations. Homophily has a variety of consequences for social and economic outcomes. Types and dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Preferential Attachment
A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. "Preferential attachment" is only the most recent of many names that have been given to such processes. They are also referred to under the names Yule process, cumulative advantage, the rich get richer, and the Matthew effect. They are also related to Gibrat's law. The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions. If preferential attachment is non-linear, measured distributions may deviate from a power law. These mechanisms may generate distributions which are approximately power law over transient periods. Definition A preferential attachment process is a stochastic urn process, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BA Model
BA, Ba, or ba may refer to: Businesses and organizations * Bangladesh Army * Bibliotheca Alexandrina, an Egyptian library and cultural center * Boeing (NYSE stock symbol BA) * Booksellers Association of the UK and Ireland * Boston Acoustics, an audio equipment manufacturer * Boston and Albany Railroad (reporting mark BA) * British Aircraft Manufacturing * British Airways (IATA airline code BA) * British-American Oil, a Canadian petroleum company * British Association for the Advancement of Science * The Nottingham Bluecoat Academy, a Church of England secondary school in Nottingham, England * Selskap med begrenset ansvar, a type of Norwegian company with limited liability * Bundesagentur für Arbeit, Federal Employment Agency of Germany Languages * Bashkir language (ISO 639 alpha-2 language code BA) * Ba (Javanese) (ꦧ), a letter in the Javanese script * Baa language, a Niger-Congo language * Aka-Bo language, an Indian language, also known as ''Ba'' * Arabic letter ب, named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Similarity Measure
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions. Use in clustering In spectral clustering, a similarity, or affinity, measure is used to transform data to overcome difficulties related to lack of convexity in the shape of the data distribut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint Probability Distribution
Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s). In the formal mathematical setup of measure theory, the joint distribution is given by the pushforward measure, by the map obtained by pairing together the given random variables, of the sample space's probability measure. In the case of real-valued random variables, the joint distribution, as a particular multivariate distribution, may be expressed by a multivariate cumulativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
