{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T21:05:32Z","timestamp":1761599132380},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2014,10,22]],"date-time":"2014-10-22T00:00:00Z","timestamp":1413936000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1007\/s11590-014-0818-7","type":"journal-article","created":{"date-parts":[[2014,10,22]],"date-time":"2014-10-22T03:01:03Z","timestamp":1413946863000},"page":"897-913","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Maximizing Barber\u2019s bipartite modularity is also hard"],"prefix":"10.1007","volume":"9","author":[{"given":"Atsushi","family":"Miyauchi","sequence":"first","affiliation":[]},{"given":"Noriyoshi","family":"Sukegawa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,10,22]]},"reference":[{"key":"818_CR1","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1140\/epjb\/e2008-00425-1","volume":"66","author":"G Agarwal","year":"2008","unstructured":"Agarwal, G., Kempe, D.: Modularity-maximizing graph communities via mathematical programming. Eur. Phys. J. B 66, 409\u2013418 (2008)","journal-title":"Eur. Phys. J. B"},{"key":"818_CR2","doi-asserted-by":"crossref","first-page":"046112","DOI":"10.1103\/PhysRevE.82.046112","volume":"82","author":"D Aloise","year":"2010","unstructured":"Aloise, D., Cafieri, S., Caporossi, G., Hansen, P., Perron, S., Liberti, L.: Column generation algorithms for exact modularity maximization in networks. Phys. Rev. E 82, 046112 (2010)","journal-title":"Phys. Rev. E"},{"key":"818_CR3","doi-asserted-by":"crossref","first-page":"066102","DOI":"10.1103\/PhysRevE.76.066102","volume":"76","author":"MJ Barber","year":"2007","unstructured":"Barber, M.J.: Modularity and community detection in bipartite networks. Phys. Rev. E 76, 066102 (2007)","journal-title":"Phys. Rev. E"},{"key":"818_CR4","doi-asserted-by":"crossref","unstructured":"Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp. P10008 (2008)","DOI":"10.1088\/1742-5468\/2008\/10\/P10008"},{"key":"818_CR5","doi-asserted-by":"crossref","first-page":"045102","DOI":"10.1103\/PhysRevE.75.045102","volume":"75","author":"S Boccaletti","year":"2007","unstructured":"Boccaletti, S., Ivanchenko, M., Latora, V., Pluchino, A., Rapisarda, A.: Detecting complex network modularity by dynamical clustering. Phys. Rev. E 75, 045102 (2007)","journal-title":"Phys. Rev. E"},{"key":"818_CR6","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/TKDE.2007.190689","volume":"20","author":"U Brandes","year":"2008","unstructured":"Brandes, U., Delling, D., Gaertler, M., G\u00f6rke, R., Hoefer, M., Nikoloski, Z., Wagner, D.: On modularity clustering. IEEE Trans. Knowl. Data Eng. 20, 172\u2013188 (2008)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"818_CR7","doi-asserted-by":"crossref","unstructured":"Cafieri, S., Costa, A., Hansen, P.: Reformulation of a model for hierarchical divisive graph modularity maximization. Ann. Oper. Res. (in press). doi: 10.1007\/s10479-012-1286-z","DOI":"10.1007\/s10479-012-1286-z"},{"key":"818_CR8","doi-asserted-by":"crossref","first-page":"056105","DOI":"10.1103\/PhysRevE.83.056105","volume":"83","author":"S Cafieri","year":"2011","unstructured":"Cafieri, S., Hansen, P., Liberti, L.: Locally optimal heuristic for modularity maximization of networks. Phys. Rev. E 83, 056105 (2011)","journal-title":"Phys. Rev. E"},{"key":"818_CR9","doi-asserted-by":"crossref","first-page":"066111","DOI":"10.1103\/PhysRevE.70.066111","volume":"70","author":"A Clauset","year":"2004","unstructured":"Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70, 066111 (2004)","journal-title":"Phys. Rev. E"},{"key":"818_CR10","doi-asserted-by":"crossref","first-page":"058101","DOI":"10.1103\/PhysRevE.84.058101","volume":"84","author":"A Costa","year":"2011","unstructured":"Costa, A., Hansen, P.: Comment on \u201cEvolutionary method for finding communities in bipartite networks\u201d. Phys. Rev. E 84, 058101 (2011)","journal-title":"Phys. Rev. E"},{"key":"818_CR11","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1007\/s11590-013-0621-x","volume":"8","author":"A Costa","year":"2014","unstructured":"Costa, A., Hansen, P.: A locally optimal hierarchical divisive heuristic for bipartite modularity maximization. Optim. Lett. 8, 903\u2013917 (2014)","journal-title":"Optim. Lett."},{"key":"818_CR12","doi-asserted-by":"crossref","first-page":"027104","DOI":"10.1103\/PhysRevE.72.027104","volume":"72","author":"J Duch","year":"2005","unstructured":"Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. Phys. Rev. E 72, 027104 (2005)","journal-title":"Phys. Rev. E"},{"key":"818_CR13","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.physrep.2009.11.002","volume":"486","author":"S Fortunato","year":"2010","unstructured":"Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75\u2013174 (2010)","journal-title":"Phys. Rep."},{"key":"818_CR14","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1073\/pnas.0605965104","volume":"104","author":"S Fortunato","year":"2007","unstructured":"Fortunato, S., Barth\u00e9lemy, M.: Resolution limit in community detection. Proc. Natl. Acad. Sci. USA 104, 36\u201341 (2007)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"818_CR15","volume-title":"Computers and intractability: a guide to the theory of NP-completeness","author":"MR Garey","year":"1979","unstructured":"Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. WH Freeman, New York (1979)"},{"key":"818_CR16","doi-asserted-by":"crossref","first-page":"046106","DOI":"10.1103\/PhysRevE.81.046106","volume":"81","author":"BH Good","year":"2010","unstructured":"Good, B.H., de Montjoye, Y.-A., Clauset, A.: Performance of modularity maximization in practical contexts. Phys. Rev. E 81, 046106 (2010)","journal-title":"Phys. Rev. E"},{"key":"818_CR17","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1038\/nature03288","volume":"433","author":"R Guimer\u00e0","year":"2005","unstructured":"Guimer\u00e0, R., Amaral, L.A.N.: Functional cartography of complex metabolic networks. Nature 433, 895\u2013900 (2005)","journal-title":"Nature"},{"key":"818_CR18","doi-asserted-by":"crossref","first-page":"036102","DOI":"10.1103\/PhysRevE.76.036102","volume":"76","author":"R Guimer\u00e0","year":"2007","unstructured":"Guimer\u00e0, R., Sales-Pardo, M., Amaral, L.A.N.: Module identification in bipartite and directed networks. Phys. Rev. E 76, 036102 (2007)","journal-title":"Phys. Rev. E"},{"key":"818_CR19","doi-asserted-by":"crossref","first-page":"046101","DOI":"10.1103\/PhysRevE.71.046101","volume":"71","author":"CP Massen","year":"2005","unstructured":"Massen, C.P., Doye, J.P.K.: Identifying communities within energy landscapes. Phys. Rev. E 71, 046101 (2005)","journal-title":"Phys. Rev. E"},{"key":"818_CR20","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.physa.2005.04.022","volume":"358","author":"AD Medus","year":"2005","unstructured":"Medus, A.D., Acu\u00f1a, G., Dorso, C.O.: Detection of community structures in networks via global optimization. Physica A 358, 593\u2013604 (2005)","journal-title":"Physica A"},{"key":"818_CR21","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1140\/epjb\/e2013-40006-7","volume":"86","author":"A Miyauchi","year":"2013","unstructured":"Miyauchi, A., Miyamoto, Y.: Computing an upper bound of modularity. Eur. Phys. J. B 86, 302 (2013)","journal-title":"Eur. Phys. J. B"},{"key":"818_CR22","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1137\/S003614450342480","volume":"45","author":"MEJ Newman","year":"2003","unstructured":"Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167\u2013256 (2003)","journal-title":"SIAM Rev."},{"key":"818_CR23","doi-asserted-by":"crossref","first-page":"8577","DOI":"10.1073\/pnas.0601602103","volume":"103","author":"MEJ Newman","year":"2006","unstructured":"Newman, M.E.J.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA 103, 8577\u20138582 (2006)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"818_CR24","volume-title":"Networks: an introduction","author":"MEJ Newman","year":"2009","unstructured":"Newman, M.E.J.: Networks: an introduction. Oxford University Press, Oxford (2009)"},{"key":"818_CR25","doi-asserted-by":"crossref","first-page":"026113","DOI":"10.1103\/PhysRevE.69.026113","volume":"69","author":"MEJ Newman","year":"2004","unstructured":"Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)","journal-title":"Phys. Rev. E"},{"key":"818_CR26","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1140\/epjb\/e2007-00331-0","volume":"60","author":"G Xu","year":"2007","unstructured":"Xu, G., Tsoka, S., Papageorgiou, L.G.: Finding community structures in complex networks using mixed integer optimisation. Eur. Phys. J. B 60, 231\u2013239 (2007)","journal-title":"Eur. Phys. J. B"},{"key":"818_CR27","doi-asserted-by":"crossref","first-page":"066120","DOI":"10.1103\/PhysRevE.83.066120","volume":"83","author":"W Zhan","year":"2011","unstructured":"Zhan, W., Zhang, Z., Guan, J., Zhou, S.: Evolutionary method for finding communities in bipartite networks. Phys. Rev. E 83, 066120 (2011)","journal-title":"Phys. Rev. E"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0818-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-014-0818-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0818-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,16]],"date-time":"2019-08-16T12:54:41Z","timestamp":1565960081000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-014-0818-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,22]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["818"],"URL":"https:\/\/doi.org\/10.1007\/s11590-014-0818-7","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,22]]}}}