The DOI matches its Crossref record.
Structural equivalence of individuals in social networks
Abstract
The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J. P., Moreno, Y., & Porter, M. A. (2014) · Journal of Complex Networks · doi:10.1093/comnet/cnu016 · Cited by 3,235
Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions
White, H. C., Boorman, S. A., & Breiger, R. L. (1976) · American Journal of Sociology · doi:10.1086/226141 · Cited by 2,097
Self-citationSocial Networks and Health: Models, Methods, and Applications
Valente, T. W. (2010) · doi:10.1093/acprof:oso/9780195301014.001.0001 · Cited by 933
How to Conduct a Mixed Methods Study: Recent Trends in a Rapidly Growing Literature
Small, M. L. (2011) · Annual Review of Sociology · doi:10.1146/annurev.soc.012809.102657 · Cited by 829
Social Structure from Multiple Networks. II. Role Structures
Boorman, S. A., & White, H. C. (1976) · American Journal of Sociology · doi:10.1086/226228 · Cited by 788
Self-citationStochastic blockmodels for directed graphs.
Wang, Y. J., & Wong, G. Y. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478385 · Cited by 480
Macrocultures: Determinants and Consequences
Abrahamson, E., & Fombrun, C. J. (1994) · The Academy of Management Review · doi:10.5465/amr.1994.9412190217 · Cited by 444
Logit models and logistic regressions for social networks: II. Multivariate relations
Pattison, P., & Wasserman, S. (1999) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711099159053 · Cited by 327
Identity Confirmation Networks and Cooperation in Work Groups
Milton, L. P., & Westphal, J. D. (2005) · Academy of Management Journal · doi:10.5465/amj.2005.16928393 · Cited by 212
Networks in Archaeology: Phenomena, Abstraction, Representation
Collar, A., Coward, F., Brughmans, T., & Mills, B. J. (2015) · Journal of Archaeological Method and Theory · doi:10.1007/s10816-014-9235-6 · Cited by 183
Network Position and Cognition in a Computer Software Firm
Walker, G. (1985) · Administrative Science Quarterly · doi:10.2307/2392814 · Cited by 129
Personality Change: Implications for Organizational Behavior
Tasselli, S., Kilduff, M., & Landis, B. (2018) · Academy of Management Annals · doi:10.5465/annals.2016.0008 · Cited by 114
Escaping the Survival Trap: Network Transition among Early-Career Freelance Songwriters
Lee, Y. G., & Gargiulo, M. (2022) · Administrative Science Quarterly · doi:10.1177/00018392211055198 · Cited by 41
Models for evolving fixed node networks: Model fitting and model testing
Sanil, A., Banks, D., & Carley, K. (1995) · Social Networks · doi:10.1016/0378-8733(94)00249-a · Cited by 28
The enigma of the kula ring: Gift-exchanges and primitive law and order
Landa, J. T. (1983) · International Review of Law and Economics · doi:10.1016/0144-8188(83)90013-3 · Cited by 24
Metadata
- Authors
- Lorrain, F., & White, H. C.
- Venue
- The Journal of Mathematical Sociology
- Publisher
- Informa UK Limited
- Published
- 1971-01
- Volume
- 1
- Issue
- 1
- Pages
- 49-80
- ISSN
- 0022-250X (ISSN-L)
- 1545-5874
- OpenAlex
- W2017099446
- Cited by
- 1,697
- References
- 0
- FWCI
- 3.25
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
