{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T14:12:35Z","timestamp":1754143955952,"version":"3.41.2"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["21K03289"],"award-info":[{"award-number":["21K03289"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Young Scientist of Japan Society for the Promotion of Science","award":["22K13963"],"award-info":[{"award-number":["22K13963"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> In this paper, we revise Conway\u2019s law from a mathematical point of view. We model it more mathematically by introducing several mathematical tools. By introducing a task graph, we first rigorously state Conway\u2019s law based on the homomorphisms in graph theory for the software system and the organizations that created it. Although Conway did not mention it, the task graph shows the geometric structure of tasks, which plays a crucial role. However, the model in terms of homomorphism is not sufficient for recent requirements for high-level treatment of communication (from security, knowledge hiding, etc.) in organizations and hierarchical treatment of organizations. In order to reformulate it for the requirement, we introduce mathematical tools, weakened homomorphisms and graph topology. Then we provide a novel mathematical model of Conway\u2019s law with hierarchical and complicated structures along the line of the recent requirement. <\/jats:p>","DOI":"10.1142\/s1793830924501027","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T08:00:58Z","timestamp":1728547258000},"source":"Crossref","is-referenced-by-count":0,"title":["Conway\u2019s law, revised from a mathematical viewpoint"],"prefix":"10.1142","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2981-0096","authenticated-orcid":false,"given":"Shigeki","family":"Matsutani","sequence":"first","affiliation":[{"name":"Electrical Engineering and Computer Science, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma Kanazawa 920-1192, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1623-9994","authenticated-orcid":false,"given":"Shousuke","family":"Ohmori","sequence":"additional","affiliation":[{"name":"National Institute of Technology, Gumma College, Maebash 371-8530, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8817-4545","authenticated-orcid":false,"given":"Kenji","family":"Hiranabe","sequence":"additional","affiliation":[{"name":"ESM, Inc., 3-111 Toiya-cho, Fukui 918-8231, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4123-9763","authenticated-orcid":false,"given":"Eiichi","family":"Hanyuda","sequence":"additional","affiliation":[{"name":"Mamezou Co., Ltd., Shinjuku-Mitsui Building 34F, 2-1-1, Nishishinjuku Shinjuku-ku, Tokyo 163-0434, Japan"},{"name":"Information-technology Promotion Agency, 2-28-8 Honkomagome, Bunkyo-ku, Tokyo 113-6591, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,11,30]]},"reference":[{"key":"S1793830924501027BIB001","first-page":"397","volume":"8","author":"Aniyany A.","year":"2023","journal-title":"Commun. 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