Transitivity correlation
| Autor: | Tom A. B. Snijders, David Krackhardt, David Dekker |
|---|---|
| Přispěvatelé: | Sociology/ICS |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
DYNAMICS
Sociology and Political Science Social Psychology MODELS 01 natural sciences Measure (mathematics) transitivity covariance 010104 statistics & probability 0504 sociology TOPOLOGY 0101 mathematics Clustering coefficient Mathematics Discrete mathematics Transitive relation Communication 05 social sciences 050401 social sciences methods Conditional probability clustering coefficient Directed graph transitive triples Covariance Reciprocity (network science) Simple function MCMC ALGORITHM network transitivity transitivity Phi transitivity correlation MATRICES |
| Zdroj: | Network Science, 7(3), 353-375. Cambridge University Press |
| ISSN: | 2050-1250 2050-1242 |
| DOI: | 10.1017/nws.2019.32 |
| Popis: | This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as comparative conditional probabilities, but these are not directly reflected by simple functions of enumerations. We think that a better approach is obtained by considering the probability of a tie between two randomly drawn nodes, conditional on selected features of the network. Two measures of transitivity based on correlation coefficients between the existence of a tie and the existence, or the number, of two-paths between the nodes are developed, and called “Transitivity Phi” and “Transitivity Correlation.” Some desirable properties for these measures are studied and compared to existing clustering coefficients, in both random (Erdös–Renyi) and in stylized networks (windmills). Furthermore, it is shown that in a directed graph, under the condition of zero Transitivity Correlation, the total number of transitive triples is determined by four underlying features: size, density, reciprocity, and the covariance between in- and outdegrees. Also, it is demonstrated that plotting conditional probability of ties, given the number of two-paths, provides valuable insights into empirical regularities and irregularities of transitivity patterns. |
| Databáze: | OpenAIRE |
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