{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T08:41:04Z","timestamp":1768725664650,"version":"3.49.0"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,12,4]],"date-time":"2014-12-04T00:00:00Z","timestamp":1417651200000},"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":["Knowl Inf Syst"],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1007\/s10115-014-0800-9","type":"journal-article","created":{"date-parts":[[2014,12,3]],"date-time":"2014-12-03T19:26:55Z","timestamp":1417634815000},"page":"617-643","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Triangle minimization in large networks"],"prefix":"10.1007","volume":"45","author":[{"given":"Rong-Hua","family":"Li","sequence":"first","affiliation":[]},{"given":"Jeffrey Xu","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,12,4]]},"reference":[{"key":"800_CR1","doi-asserted-by":"crossref","unstructured":"Albert R et al (2000) Error and attack tolerance of complex networks. Nature 406:378\u2013382","DOI":"10.1038\/35019019"},{"key":"800_CR2","doi-asserted-by":"crossref","unstructured":"Alon N et al (1997) Finding and counting given length cycles. Algorithmica 17(3):209\u2013223","DOI":"10.1007\/BF02523189"},{"key":"800_CR3","unstructured":"Avron H (2010) Counting triangles in large graphs using randomized matrix trace estimation. In: Proceedings of KDD-LDMTA\u201910"},{"key":"800_CR4","unstructured":"Bar-Yossef Z et al (2002) Reductions in streaming algorithms, with an application to counting triangles in graphs. In: SODA"},{"key":"800_CR5","doi-asserted-by":"crossref","unstructured":"Barabasi A-L, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509\u2013512","DOI":"10.1126\/science.286.5439.509"},{"key":"800_CR6","doi-asserted-by":"crossref","unstructured":"Becchetti L et al (2008) Efficient semi-streaming algorithms for local triangle counting in massive graphs. In: KDD","DOI":"10.1145\/1401890.1401898"},{"key":"800_CR7","unstructured":"Brin S, Page L (1997) PageRank: bringing order to the web. Tech. rep, Stanford Digital Library Project"},{"key":"800_CR8","doi-asserted-by":"crossref","unstructured":"Buriol LS et al (2006) Counting triangles in data streams. In: PODS","DOI":"10.1145\/1142351.1142388"},{"key":"800_CR9","doi-asserted-by":"crossref","unstructured":"Callaway DS et al (2000) Network robustness and fragility: percolation on random graphs. Phys Rev Lett 85(25):5468\u20135471","DOI":"10.1103\/PhysRevLett.85.5468"},{"key":"800_CR10","doi-asserted-by":"crossref","unstructured":"Chu S, Cheng J (2011) Triangle listing in massive networks and its applications. In: KDD","DOI":"10.1145\/2020408.2020513"},{"key":"800_CR11","doi-asserted-by":"crossref","unstructured":"Cohen R et al (2000) Resilience of the internet to random breakdowns. Phys Rev Lett 85(21):5626\u20135628","DOI":"10.1103\/PhysRevLett.85.4626"},{"key":"800_CR12","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1086\/228943","volume":"94","author":"JS Coleman","year":"1988","unstructured":"Coleman JS (1988) Social capital in the creation of human capital. Am J Sociol 94:95\u2013120","journal-title":"Am J Sociol"},{"key":"800_CR13","unstructured":"Durand M, Flajolet P (2003) Loglog counting of large cardinalities (extended abstract). In: ESA, pp 605\u2013617"},{"key":"800_CR14","doi-asserted-by":"crossref","unstructured":"Feige U (1998) A threshold of in n for approximating set cover. J ACM 45(4):634\u2013652","DOI":"10.1145\/285055.285059"},{"key":"800_CR15","unstructured":"Flajolet P et al (2003) Hyperloglog: the analysis of a near-optimal cardinality estimation algorithm. In: ESA, pp 605\u2013617"},{"issue":"2","key":"800_CR16","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/0022-0000(85)90041-8","volume":"31","author":"P Flajolet","year":"1985","unstructured":"Flajolet P, Martin GN (1985) Probabilistic counting algorithms for data base applications. J Comput Syst Sci 31(2):182\u2013209","journal-title":"J Comput Syst Sci"},{"key":"800_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic graph theory","author":"C Godsil","year":"2001","unstructured":"Godsil C, Royle GF (2001) Algebraic graph theory. Springer, Berlin"},{"key":"800_CR18","unstructured":"Hanneman RA, Riddle M (2005) Introduction to social network methods. University of California, Riverside. http:\/\/faculty.ucr.edu\/~hanneman\/nettext\/"},{"key":"800_CR19","unstructured":"Hochbaum DS (1996) Approximation algorithms for NP-hard problems. PWS Publishing Company, Boston, MA"},{"key":"800_CR20","doi-asserted-by":"crossref","unstructured":"Itai A, Rodeh M (1978) Finding a minimum circuit in a graph. SIAM J Comput 7(4):413\u2013423","DOI":"10.1137\/0207033"},{"key":"800_CR21","doi-asserted-by":"crossref","unstructured":"Jowhari H, Ghodsi M (2005) New streaming algorithms for counting triangles in graphs. In: COCOON","DOI":"10.1007\/11533719_72"},{"key":"800_CR22","doi-asserted-by":"crossref","unstructured":"Kempe D et al (2003) Maximizing the spread of influence through a social network. In: KDD","DOI":"10.1145\/956750.956769"},{"key":"800_CR23","unstructured":"Krause A, Guestrin C (2007) Near-optimal observation selection using submodular functions. In: AAAI"},{"key":"800_CR24","unstructured":"Krause A, Horvitz E (2008) A utility-theoretic approach to privacy and personalization. In: AAAI"},{"key":"800_CR25","unstructured":"Krause A et al (2008) Near-optimal sensor placements in Gaussian processes: theory, efficient algorithms and empirical studies. J Mach Learn Res 9:235\u2013284"},{"key":"800_CR26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tcs.2008.07.017","volume":"407","author":"M Latapy","year":"2008","unstructured":"Latapy M (2008) Main-memory triangle computations for very large (sparse (power-law)) graphs. Theor Comput Sci 407:1\u20133","journal-title":"Theor Comput Sci"},{"key":"800_CR27","unstructured":"Leskovec J (2010) Standford network analysis project"},{"key":"800_CR28","doi-asserted-by":"crossref","unstructured":"Leskovec J et al (2007) Cost-effective outbreak detection in networks. In: KDD","DOI":"10.1145\/1281192.1281239"},{"key":"800_CR29","doi-asserted-by":"crossref","unstructured":"Li R-H, Yu JX (2011) Scalable diversified ranking on large graphs. In: ICDM","DOI":"10.1109\/ICDM.2011.126"},{"issue":"9","key":"800_CR30","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1109\/TKDE.2012.170","volume":"25","author":"R-H Li","year":"2013","unstructured":"Li R-H, Yu JX (2013) Scalable diversified ranking on large graphs. IEEE Trans Knowl Data Eng 25(9):2133\u20132146","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"800_CR31","doi-asserted-by":"crossref","unstructured":"Li R-H et al (2014a) Random-walk domination in large graphs. In: ICDE","DOI":"10.1109\/ICDE.2014.6816696"},{"key":"800_CR32","doi-asserted-by":"crossref","unstructured":"Li R-H et al (2012) Measuring robustness of complex networks under MVC attack. In: CIKM","DOI":"10.1145\/2396761.2398463"},{"key":"800_CR33","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.ins.2014.03.085","volume":"278","author":"R-H Li","year":"2014","unstructured":"Li R-H et al (2014b) Measuring the impact of MVC attack in large complex networks. Inf Sci 278:685\u2013702","journal-title":"Inf Sci"},{"key":"800_CR34","unstructured":"Lin H, Bilmes J (2010) Multi-document summarization via budgeted maximization of submodular functions. In: HLT-NAACL"},{"key":"800_CR35","unstructured":"Lin H, Bilmes J (2011) A class of submodular functions for document summarization. In: ACL"},{"key":"800_CR36","doi-asserted-by":"crossref","unstructured":"McPherson M et al (2001) Birds of a feather: homophily in social networks. Annu Rev Sociol 27:415\u2013444","DOI":"10.1146\/annurev.soc.27.1.415"},{"key":"800_CR37","unstructured":"Minoux M (1978) Accelerated greedy algorithms for maximizing submodular set functions. Lecture Notes in Control and Information Sciences. Springer, Berlin"},{"key":"800_CR38","doi-asserted-by":"crossref","unstructured":"Nemhauser GL et al (1978) An analysis of approximations for maximizing submodular set functions-I. Math Program 14:265\u2013294","DOI":"10.1007\/BF01588971"},{"key":"800_CR39","doi-asserted-by":"crossref","unstructured":"Palmer CR et al (2002) ANF: a fast and scalable tool for data mining in massive graphs. In: KDD, pp 81\u201390","DOI":"10.1145\/775047.775059"},{"key":"800_CR40","unstructured":"Schank T (2007) Algorithmic aspects of triangle-based network analysis. PhD Thesis, University Karlsruhe (TH)"},{"key":"800_CR41","doi-asserted-by":"crossref","unstructured":"Schank T, Wagner D (2005) Finding, counting and listing all triangles in large graphs, an experimental study. In: WEA","DOI":"10.1007\/11427186_54"},{"key":"800_CR42","doi-asserted-by":"crossref","unstructured":"Schneider CM et al (2011) Mitigation of malicious attacks on networks. PNAS 108(10):3838\u20133841","DOI":"10.1073\/pnas.1009440108"},{"key":"800_CR43","unstructured":"Seshadhri C et al (2012) Fast triangle counting through wedge sampling. CoRR abs\/1202.5230"},{"key":"800_CR44","doi-asserted-by":"crossref","unstructured":"Suri S, Vassilvitskii S (2011) Counting triangles and the curse of the last reducer. In: WWW","DOI":"10.1145\/1963405.1963491"},{"key":"800_CR45","doi-asserted-by":"crossref","unstructured":"Tong H et al (2012) Gelling, and melting, large graphs by edge manipulation. In: CIKM","DOI":"10.1145\/2396761.2396795"},{"key":"800_CR46","doi-asserted-by":"crossref","unstructured":"Tong H et al (2010) On the vulnerability of large graphs. In: ICDM","DOI":"10.1109\/ICDM.2010.54"},{"key":"800_CR47","doi-asserted-by":"crossref","unstructured":"Tsourakakis CE et al (2009) DOULION: counting triangles in massive graphs with a coin. In: KDD","DOI":"10.1145\/1557019.1557111"},{"key":"800_CR48","unstructured":"Vazirani VV (2001) Approximation algorithms. Springer, Berlin"},{"key":"800_CR49","first-page":"253","volume":"B23","author":"J Vondrak","year":"2010","unstructured":"Vondrak J (2010) Submodularity and curvature: the optimal algorithm. RIMS Kokyuroku Bessatsu B23:253\u2013266","journal-title":"RIMS Kokyuroku Bessatsu"},{"key":"800_CR50","doi-asserted-by":"crossref","unstructured":"Watts DJ, Strogatz SH (1998) Collective dynamics of \u2019small-world\u2019 networks. Nature 393:440\u2013442","DOI":"10.1038\/30918"},{"key":"800_CR51","unstructured":"Zafarani R, Liu H (2009) Social Computing Data Repository at ASU"}],"container-title":["Knowledge and Information Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10115-014-0800-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10115-014-0800-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10115-014-0800-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T10:11:16Z","timestamp":1559124676000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10115-014-0800-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,4]]},"references-count":51,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["800"],"URL":"https:\/\/doi.org\/10.1007\/s10115-014-0800-9","relation":{},"ISSN":["0219-1377","0219-3116"],"issn-type":[{"value":"0219-1377","type":"print"},{"value":"0219-3116","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,4]]}}}