{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:42:05Z","timestamp":1780386125587,"version":"3.54.1"},"publisher-location":"Cham","reference-count":28,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031853623","type":"print"},{"value":"9783031853630","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-85363-0_6","type":"book-chapter","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T08:50:45Z","timestamp":1741078245000},"page":"81-99","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Clustering the\u00a0Nodes of\u00a0Sparse Edge-Weighted Graphs via\u00a0Non-backtracking Spectra"],"prefix":"10.1007","author":[{"given":"Marianna","family":"Bolla","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hannu","family":"Reittu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fatma","family":"Abdelkhalek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,3,5]]},"reference":[{"key":"6_CR1","doi-asserted-by":"crossref","unstructured":"Chung, F.: Spectral Graph Theory, CBMS Regional Conference Series in Mathematics 92. American Mathematical Society, Providence RI (1997)","DOI":"10.1090\/cbms\/092"},{"key":"6_CR2","doi-asserted-by":"crossref","unstructured":"Newman, M.E.J.: Networks, An Introduction. Oxford University Press (2010)","DOI":"10.1093\/acprof:oso\/9780199206650.003.0001"},{"key":"6_CR3","doi-asserted-by":"crossref","unstructured":"Bolla, M.: Spectral Clustering and Biclusterig. Wiley (2013)","DOI":"10.1002\/9781118650684"},{"issue":"4","key":"6_CR4","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1088\/1361-6544\/ab60d2","volume":"33","author":"M Bolla","year":"2020","unstructured":"Bolla, M.: Generalized quasirandom properties of expanding graph sequences. Nonlinearity 33(4), 1405\u20131424 (2020)","journal-title":"Nonlinearity"},{"key":"6_CR5","doi-asserted-by":"crossref","unstructured":"Bordenave, C., Lelarge, M., Massouli\u00e9, L.: Non-backtracking spectrum of random graphs: community detection and non-regular Ramanujan graphs. Ann. Probab. 46(1), 1\u201371 (2018)","DOI":"10.1214\/16-AOP1142"},{"key":"6_CR6","doi-asserted-by":"crossref","unstructured":"Stephan, L., Massouli\u00e9, L.: Non-backtracking spectra of inhomogeneous random graphs. Math. Stat. Learn. 5(3), 201\u2013271 (2022)","DOI":"10.4171\/msl\/34"},{"issue":"1","key":"6_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/08-AOP394","volume":"37","author":"M Capitaine","year":"2009","unstructured":"Capitaine, M., Donati-Martin, C., F\u00e9ral, D.: The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations. Ann. Probab. 37(1), 1\u201347 (2009)","journal-title":"Ann. Probab."},{"issue":"03","key":"6_CR8","doi-asserted-by":"publisher","first-page":"2150028","DOI":"10.1142\/S2010326321500283","volume":"10","author":"S Coste","year":"2021","unstructured":"Coste, S., Zhu, Y.: Eigenvalues of the non-backtracking operator detached from the bulk. Random Matrices Theory Appl. 10(03), 2150028 (2021)","journal-title":"Random Matrices Theory Appl."},{"key":"6_CR9","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.laa.2023.10.014","volume":"680","author":"R Mulas","year":"2024","unstructured":"Mulas, R., Zhang, D., Zucal, G.: There is no going back: properties of the non-backtracking Laplacian. Linear Algebra Appl. 680, 341\u2013370 (2024)","journal-title":"Linear Algebra Appl."},{"key":"6_CR10","unstructured":"Torres, L.: Geometric multiplicity of unitary non-backrtacking eigenvalues. Preprint, arXiv:2205.02004v1 [math.CO] (2022)"},{"issue":"2","key":"6_CR11","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1137\/20M1352132","volume":"3","author":"L Torres","year":"2021","unstructured":"Torres, L., Chan, K.S., Tong, H., Eliassi-Rad, T.: Nonbacktracking eigenvalues under node removal: X-centrality and targeted immunisation. SIAM J. Math. Data Sci. 3(2), 656\u2013675 (2021)","journal-title":"SIAM J. Math. Data Sci."},{"key":"6_CR12","doi-asserted-by":"crossref","unstructured":"Achlioptas, D., McSherry, F.: Fast computation of low-rank matrix approximations. J. ACM 54(2), Article 9 (2007)","DOI":"10.1145\/1219092.1219097"},{"key":"6_CR13","first-page":"4099","volume":"11","author":"SM Mniszewski","year":"2021","unstructured":"Mniszewski, S.M., et al.: Reduction of the molecular hamiltonian matrix using quantum community detection. Sci. Rep. Nature 11, 4099 (2021)","journal-title":"Sci. Rep. Nature"},{"key":"6_CR14","unstructured":"Watanabe, Y., Fukumizu, K.: Graph zeta function in the bethe free energy and loopy belief propagation. In: Bengio, Y., Schuurmans, D., Lafferty, J.D., Williams, C.K.I., Culotta, A. (eds.) Advances in Neural Information Processing Systems 22, pp. 2017\u20132025. Curran Associates Inc. (2010)"},{"key":"6_CR15","unstructured":"Bolla, M., Zhou, D.: Percolated stochastic block model via EM algorithm and belief propagation with non-backtracking spectra. Preprint, arXiv:2307.16502v6 [math.CO] (2023)"},{"issue":"3","key":"6_CR16","doi-asserted-by":"publisher","first-page":"2141","DOI":"10.1214\/19-AIHP1033","volume":"56","author":"F Benaych-Georges","year":"2020","unstructured":"Benaych-Georges, F., Bordenave, C., Knowles, A.: Spectral radii of sparse random matrices. Ann. Inst. Henri Poincar\u00e9 Probab. Stat. 56(3), 2141\u20132161 (2020)","journal-title":"Ann. Inst. Henri Poincar\u00e9 Probab. Stat."},{"key":"6_CR17","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.laa.2021.01.022","volume":"618","author":"C Glover","year":"2021","unstructured":"Glover, C., Kempton, M.: Some spectral properties of the non-backtracking matrix of a graph. Linear Algebra Appl. 618, 37\u201357 (2021)","journal-title":"Linear Algebra Appl."},{"key":"6_CR18","doi-asserted-by":"publisher","first-page":"20935","DOI":"10.1073\/pnas.1312486110","volume":"110","author":"F Krzakala","year":"2013","unstructured":"Krzakala, F., et al.: Spectral redemption in clustering sparse networks. Proc. Nat. Acad. Sci. USA 110, 20935\u201320940 (2013)","journal-title":"Proc. Nat. Acad. Sci. USA"},{"issue":"06","key":"6_CR19","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1142\/S0129167X92000357","volume":"03","author":"H Bass","year":"1992","unstructured":"Bass, H.: The Ihara-Selberg zeta function of a tree lattice. Int. J. Math. 03(06), 717\u2013797 (1992)","journal-title":"Int. J. Math."},{"key":"6_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.065701","volume":"107","author":"A Decelle","year":"2011","unstructured":"Decelle, A., Krzakala, F., Moore, C., Zdeborov\u00e1, L.: Inference and phase transitions in the detection of modules in sparse networks. Phys. Rev. Lett. 107, 065701 (2011)","journal-title":"Phys. Rev. Lett."},{"key":"6_CR21","doi-asserted-by":"crossref","unstructured":"Abbe, E., Sandon, C.: Community detection in general stochastic block models: fundamental limits and efficient algorithms for recovery. In: 2015 IEEE 56th Annual Symposium on FOCS (2015)","DOI":"10.1109\/FOCS.2015.47"},{"issue":"177","key":"6_CR22","first-page":"1","volume":"18","author":"E Abbe","year":"2018","unstructured":"Abbe, E.: Community detection in general stochastic block models: recent developments. J. Mach. Learn. Res. 18(177), 1\u201386 (2018)","journal-title":"J. Mach. Learn. Res."},{"key":"6_CR23","unstructured":"Moore, C.: The computer science and physics of community detection: landscapes, phase transitions, and hardness. Bull. EATCS 121 (2017)"},{"key":"6_CR24","first-page":"20220774","volume":"479","author":"MEJ Newman","year":"2023","unstructured":"Newman, M.E.J.: Message passing methods on complex networks. Proc. R. Soc. London A 479, 20220774 (2023)","journal-title":"Proc. R. Soc. London A"},{"key":"6_CR25","first-page":"17","volume":"5","author":"P Erd\u0151s","year":"1960","unstructured":"Erd\u0151s, P., R\u00e9nyi, A.: On the evolution of random graphs. Publ. Math. Inst. HAS 5, 17\u201361 (1960)","journal-title":"Publ. Math. Inst. HAS"},{"key":"6_CR26","unstructured":"Toloui, B., Love, P.: Quantum algorithms for quantum chemistry based on the sparsity of the CI-matrix. Preprint, arXiv:1312.2579v2 [quant-ph] (2013)"},{"issue":"3","key":"6_CR27","doi-asserted-by":"publisher","first-page":"806","DOI":"10.1007\/s10910-016-0591-1","volume":"54","author":"P \u00c1rend\u00e1s","year":"2016","unstructured":"\u00c1rend\u00e1s, P., Furtenbacher, T., Cs\u00e1sz\u00e1r, A.G.: On spectra of spectra. J. Math. Chem. 54(3), 806\u2013822 (2016). https:\/\/doi.org\/10.1007\/s10910-016-0591-1","journal-title":"J. Math. Chem."},{"issue":"1","key":"6_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13660-015-0632-5","volume":"2015","author":"H Wang","year":"2015","unstructured":"Wang, H., Huang, J., Chen, A.: Eigenvalue problem of Hamiltonian operator matrices. J. Inequalities Appl. 2015(1), 1\u201313 (2015). https:\/\/doi.org\/10.1186\/s13660-015-0632-5","journal-title":"J. Inequalities Appl."}],"container-title":["Lecture Notes in Networks and Systems","Advances in Information and Communication"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-85363-0_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T08:50:54Z","timestamp":1741078254000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-85363-0_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031853623","9783031853630"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-85363-0_6","relation":{},"ISSN":["2367-3370","2367-3389"],"issn-type":[{"value":"2367-3370","type":"print"},{"value":"2367-3389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"5 March 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FICC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Future of Information and Communication Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Berlin","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 April 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 April 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ficc2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/saiconference.com\/FICC","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}