{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:40Z","timestamp":1753893820532,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the response matrices in certain weighted networks that display a circular symmetry.\u00a0It had been observed empirically that these exhibit several paired (multiplicity two) eigenvalues.\u00a0Here, this pairing is explained analytically for a version of the model more general than the original.\u00a0The exact number of necessarily paired eigenvalues is given in terms of the structure of the model,\u00a0and the special structure of the eigenvectors is also described. Examples are provided.<\/jats:p>","DOI":"10.37236\/3318","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:23:56Z","timestamp":1578705836000},"source":"Crossref","is-referenced-by-count":1,"title":["Eigenvalue Pairing in the Response Matrix for a Class of Network Models with Circular Symmetry"],"prefix":"10.37236","volume":"20","author":[{"given":"Miriam","family":"Farber","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles R","family":"Johnson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Zhen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,8,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:16:08Z","timestamp":1579259768000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,9]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/3318","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,8,9]]},"article-number":"P17"}}