On the relation between Markov random fields and social networks
Bibliographic Data
| ID | 7516793 |
|---|---|
| Authors | Ross Kindermann (University of Nebraska–Lincoln, corresponding author), Ross P Kindermann, J Laurie Snell (Dartmouth College) |
| Year | 1980 |
| Volume | 7 |
| Issue | 1 |
| Pages | 1-13 |
| Publication date | 1980-05-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Journal of Mathematical Sociology (JOURNAL) |
| Journal identifiers | ISSN: 0022-250X • E-ISSN: 1545-5874 |
| Publisher | Taylor & Francis (PUBLISHER • GB) |
| DOI | 10.1080/0022250x.1980.9989895 |
| OpenAlex | W2032414074 |
| Language | EN |
| Citations received | 8 |
| References cited | 10 |
Holland and Leinhardt (1977a) introduced a continuous time Markov chain to model changes in a social network. Their model was further studied by Wasserman (1977). Holland and Leinhardt (1977b) have also proposed a general class of probability measures on random networks. The purpose of this paper is to show that these probability measures may be viewed as Gibbs measures induced by a nearest neighbor potential. As such they have a Markov field property which is a natural generalization of Markov chains to spatial situations. The dynamic models are shown to fit into a general class of Markov processes suggested by the study of interacting particle systems. A related “voter model” is discussed
Class (philosophy · Discrete mathematics · Generalization · Markov chain · Markov model · Markov process · Markov property · Markov renewal process · Mathematical analysis · Physics · Random field · Statistical physics · Statistics · Variable-order Markov model · Artificial Intelligence · Complex Network Analysis Techniques · Computer Science · Evolutionary Game Theory and Cooperation · Mathematics · Opinion Dynamics and Social Influence
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| Unique citing works | 8 |
|---|---|
| Citations per year | 0,18 |
| Citation span | 1981 - 2021 (41) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 7 |