{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:20Z","timestamp":1740109580581,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T00:00:00Z","timestamp":1593993600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T00:00:00Z","timestamp":1593993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s00454-020-00218-8","type":"journal-article","created":{"date-parts":[[2020,7,6]],"date-time":"2020-07-06T14:03:53Z","timestamp":1594044233000},"page":"116-142","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Number of Weakly Connected Subdigraphs in Random kNN Digraphs"],"prefix":"10.1007","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1533-7194","authenticated-orcid":false,"given":"Selim","family":"Bahad\u0131r","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2423-3178","authenticated-orcid":false,"given":"Elvan","family":"Ceyhan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,6]]},"reference":[{"issue":"4","key":"218_CR1","doi-asserted-by":"publisher","first-page":"1033","DOI":"10.1214\/aoap\/1177005271","volume":"3","author":"F Avram","year":"1993","unstructured":"Avram, F., Bertsimas, D.: On central limit theorems in geometrical probability. Ann. Appl. Probab. 3(4), 1033\u20131046 (1993)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"218_CR2","doi-asserted-by":"publisher","first-page":"123","DOI":"10.19195\/0208-4147.38.1.7","volume":"38","author":"S Bahad\u0131r","year":"2018","unstructured":"Bahad\u0131r, S., Ceyhan, E.: On the number of reflexive and shared nearest neighbor pairs in one-dimensional uniform data. Probab. Math. Stat. 38(1), 123\u2013137 (2018)","journal-title":"Probab. Math. Stat."},{"issue":"1","key":"218_CR3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1214\/aop\/1176993668","volume":"11","author":"PJ Bickel","year":"1983","unstructured":"Bickel, P.J., Breiman, L.: Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test. Ann. Probab. 11(1), 185\u2013214 (1983)","journal-title":"Ann. Probab."},{"key":"218_CR4","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.jmva.2012.12.007","volume":"116","author":"MR Brito","year":"2013","unstructured":"Brito, M.R., Quiroz, A.J., Yukich, J.E.: Intrinsic dimension identification via graph-theoretic methods. J. Multivariate Anal. 116, 263\u2013277 (2013)","journal-title":"J. Multivariate Anal."},{"issue":"8","key":"218_CR5","doi-asserted-by":"publisher","first-page":"2786","DOI":"10.1016\/j.csda.2008.08.002","volume":"53","author":"E Ceyhan","year":"2009","unstructured":"Ceyhan, E.: Overall and pairwise segregation tests based on nearest neighbor contingency tables. Comput. Stat. Data Anal. 53(8), 2786\u20132808 (2009)","journal-title":"Comput. Stat. Data Anal."},{"doi-asserted-by":"crossref","unstructured":"Ceyhan, E.: Testing spatial symmetry using contingency tables based on nearest neighbor relations. Sci. World J. 2014, # 698296 (2014)","key":"218_CR6","DOI":"10.1155\/2014\/698296"},{"issue":"1","key":"218_CR7","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10651-016-0361-z","volume":"24","author":"E Ceyhan","year":"2017","unstructured":"Ceyhan, E., Bahad\u0131r, S.: Nearest neighbor methods for testing reflexivity. Environ. Ecol. Stat. 24(1), 69\u2013108 (2017)","journal-title":"Environ. Ecol. Stat."},{"key":"218_CR8","volume-title":"Graphs & Digraphs","author":"G Chartrand","year":"1996","unstructured":"Chartrand, G., Lesniak, L.: Graphs & Digraphs. Chapman & Hall, London (1996)"},{"issue":"3142","key":"218_CR9","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1126\/science.121.3142.397","volume":"121","author":"PJ Clark","year":"1955","unstructured":"Clark, P.J., Evans, F.C.: On some aspects of spatial pattern in biological populations. Science 121(3142), 397\u2013398 (1955)","journal-title":"Science"},{"doi-asserted-by":"crossref","unstructured":"Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups. Grundlehren der Mathematischen Wissenschaften, vol. 290. Springer, New York (1988)","key":"218_CR10","DOI":"10.1007\/978-1-4757-2016-7"},{"issue":"2","key":"218_CR11","doi-asserted-by":"publisher","first-page":"367","DOI":"10.2307\/2530424","volume":"37","author":"TF Cox","year":"1981","unstructured":"Cox, T.F.: Reflexive nearest neighbors. Biometrics 37(2), 367\u2013369 (1981)","journal-title":"Biometrics"},{"issue":"1","key":"218_CR12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1111\/j.2517-6161.1990.tb01773.x","volume":"52","author":"J Cuzick","year":"1990","unstructured":"Cuzick, J., Edwards, R.: Spatial clustering for inhomogeneous populations. With discussion and a reply by the authors. J. R. Stat. Soc. Ser. B 52(1), 73\u2013104 (1990)","journal-title":"J. R. Stat. Soc. Ser. B"},{"issue":"1","key":"218_CR13","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1111\/j.1467-8306.1960.tb00332.x","volume":"50","author":"MF Dacey","year":"1960","unstructured":"Dacey, M.F.: The spacing of river towns. Ann. Assoc. Am. Geogr. 50(1), 59\u201361 (1960)","journal-title":"Ann. Assoc. Am. Geogr."},{"issue":"7","key":"218_CR14","doi-asserted-by":"publisher","first-page":"1940","DOI":"10.2307\/1941598","volume":"75","author":"P Dixon","year":"1994","unstructured":"Dixon, P.: Testing spatial segregation using a nearest-neighbor contingency table. Ecology 75(7), 1940\u20131948 (1994)","journal-title":"Ecology"},{"issue":"2","key":"218_CR15","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1080\/11956860.2002.11682700","volume":"9","author":"PM Dixon","year":"2002","unstructured":"Dixon, P.M.: Nearest-neighbor contingency table analysis of spatial segregation for several species. \u00c9coscience 9(2), 142\u2013151 (2002)","journal-title":"\u00c9coscience"},{"issue":"4","key":"218_CR16","doi-asserted-by":"publisher","first-page":"843","DOI":"10.2307\/3316135","volume":"27","author":"EG Enns","year":"1999","unstructured":"Enns, E.G., Ehlers, P.F., Misi, T.: A cluster problem as defined by nearest neighbours. Can. J. Stat. 27(4), 843\u2013851 (1999)","journal-title":"Can. J. Stat."},{"issue":"3","key":"218_CR17","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/PL00009293","volume":"17","author":"D Eppstein","year":"1997","unstructured":"Eppstein, D., Paterson, M.S., Yao, F.F.: On nearest-neighbor graphs. Discrete Comput. Geom. 17(3), 263\u2013282 (1997)","journal-title":"Discrete Comput. Geom."},{"unstructured":"Erd\u0151s, P., R\u00e9nyi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutat\u00f3 Int. K\u00f6zl. 5, 17\u201361 (1960)","key":"218_CR18"},{"issue":"2","key":"218_CR19","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1214\/aos\/1176346148","volume":"11","author":"JH Friedman","year":"1983","unstructured":"Friedman, J.H., Rafsky, L.C.: Graph-theoretic measures of multivariate association and prediction. Ann. Stat. 11(2), 377\u2013391 (1983)","journal-title":"Ann. Stat."},{"issue":"4","key":"218_CR20","doi-asserted-by":"publisher","first-page":"873","DOI":"10.2307\/1427106","volume":"19","author":"N Henze","year":"1987","unstructured":"Henze, N.: On the fraction of random points with specified nearest-neighbour interrelations and degree of attraction. Adv. Appl. Probab. 19(4), 873\u2013895 (1987)","journal-title":"Adv. Appl. Probab."},{"key":"218_CR21","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/BF02771528","volume":"142","author":"S Janson","year":"2004","unstructured":"Janson, S., Oleszkiewicz, K., Ruci\u0144ski, A.: Upper tails for subgraph counts in random graphs. Isr. J. Math. 142, 61\u201392 (2004)","journal-title":"Isr. J. Math."},{"issue":"1","key":"218_CR22","first-page":"3","volume":"14","author":"GA Kabatiansky","year":"1978","unstructured":"Kabatiansky, G.A., Levenshtein, V.I.: On bounds for packings on a sphere and in space. Probl. Peredachi Inf. 14(1), 3\u201325 (1978). (in Russian)","journal-title":"Probl. Peredachi Inf."},{"issue":"2","key":"218_CR23","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1214\/18-AAP1405","volume":"29","author":"R Lachi\u00e8ze-Rey","year":"2019","unstructured":"Lachi\u00e8ze-Rey, R., Schulte, M., Yukich, J.E.: Normal approximation for stabilizing functionals. Ann. Appl. Probab. 29(2), 931\u2013993 (2019)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"218_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4007\/annals.2008.168.1","volume":"168","author":"OR Musin","year":"2008","unstructured":"Musin, O.R.: The kissing number in four dimensions. Ann. Math. 168(1), 1\u201332 (2008)","journal-title":"Ann. Math."},{"unstructured":"Najim, Ch.A., Russo, R.P.: On the number of subgraphs of a specified form embedded in a random graph. Methodol. Comput. Appl. Probab. 5(1), 23\u201333 (2003)","key":"218_CR25"},{"issue":"4","key":"218_CR26","doi-asserted-by":"publisher","first-page":"726","DOI":"10.2307\/1427321","volume":"15","author":"CM Newman","year":"1983","unstructured":"Newman, C.M., Rinott, Y., Tversky, A.: Nearest neighbors and Voronoi regions in certain point processes. Adv. Appl. Probab. 15(4), 726\u2013751 (1983)","journal-title":"Adv. Appl. Probab."},{"issue":"1\u20133","key":"218_CR27","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/0012-365X(88)90220-8","volume":"72","author":"K Nowicki","year":"1988","unstructured":"Nowicki, K., Wierman, J.C.: Subgraph counts in random graphs using incomplete $$U$$-statistics methods. Discrete Math. 72(1\u20133), 299\u2013310 (1988)","journal-title":"Discrete Math."},{"key":"218_CR28","series-title":"Oxford Studies in Probability","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198506263.001.0001","volume-title":"Random Geometric Graphs","author":"M Penrose","year":"2003","unstructured":"Penrose, M.: Random Geometric Graphs. Oxford Studies in Probability, vol. 5. Oxford University Press, Oxford (2003)"},{"key":"218_CR29","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1214\/EJP.v12-429","volume":"12","author":"MD Penrose","year":"2007","unstructured":"Penrose, M.D.: Gaussian limits for random geometric measures. Electron. J. Probab. 12, 989\u20131035 (2007)","journal-title":"Electron. J. Probab."},{"issue":"4","key":"218_CR30","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1214\/aoap\/1015345393","volume":"11","author":"MD Penrose","year":"2001","unstructured":"Penrose, M.D., Yukich, J.E.: Central limit theorems for some graphs in computational geometry. Ann. Appl. Probab. 11(4), 1005\u20131041 (2001)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"218_CR31","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1214\/aoap\/1015961164","volume":"12","author":"MD Penrose","year":"2002","unstructured":"Penrose, M.D., Yukich, J.E.: Limit theory for random sequential packing and deposition. Ann. Appl. Probab. 12(1), 272\u2013301 (2002)","journal-title":"Ann. Appl. Probab."},{"key":"218_CR32","first-page":"37","volume-title":"In: Stein\u2019s Method and Applications. Lecture Notes Series, Institute for Mathematical Sciences","author":"MD Penrose","year":"2005","unstructured":"Penrose, M.D., Yukich, J.E.: Normal approximation in geometric probability. In: Stein\u2019s Method and Applications. Lecture Notes Series, Institute for Mathematical Sciences, vol. 5, pp. 37\u201358. Singapore University Press, Singapore (2005)"},{"issue":"2","key":"218_CR33","doi-asserted-by":"publisher","first-page":"444","DOI":"10.2307\/3213499","volume":"19","author":"DK Pickard","year":"1982","unstructured":"Pickard, D.K.: Isolated nearest neighbors. J. Appl. Probab. 19(2), 444\u2013449 (1982)","journal-title":"J. Appl. Probab."},{"issue":"2","key":"218_CR34","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1093\/biomet\/56.2.401","volume":"56","author":"FDK Roberts","year":"1969","unstructured":"Roberts, F.D.K.: Nearest neighbours in a Poisson ensemble. Biometrika 56(2), 401\u2013406 (1969)","journal-title":"Biometrika"},{"issue":"1","key":"218_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF00718031","volume":"78","author":"A Ruci\u0144ski","year":"1988","unstructured":"Ruci\u0144ski, A.: When are small subgraphs of a random graph normally distributed? Probab. Theory Relat. Fields 78(1), 1\u201310 (1988)","journal-title":"Probab. Theory Relat. Fields"},{"issue":"2","key":"218_CR36","doi-asserted-by":"publisher","first-page":"388","DOI":"10.2307\/1427305","volume":"18","author":"MF Schilling","year":"1986","unstructured":"Schilling, M.F.: Mutual and shared neighbor probabilities: finite- and infinite-dimensional results. Adv. Appl. Probab. 18(2), 388\u2013405 (1986)","journal-title":"Adv. Appl. Probab."},{"issue":"2","key":"218_CR37","first-page":"69","volume":"2","author":"Y Shang","year":"2010","unstructured":"Shang, Y.: Laws of large numbers of subgraphs in directed random geometric networks. Int. Electron. J. Pure Appl. Math. 2(2), 69\u201379 (2010)","journal-title":"Int. Electron. J. Pure Appl. Math."},{"doi-asserted-by":"crossref","unstructured":"Trinh, K.D.: On central limit theorems in stochastic geometry for add-one cost stabilizing functionals. Electron. Commun. Probab. 24, # 76 (2019)","key":"218_CR38","DOI":"10.1214\/19-ECP279"},{"issue":"2","key":"218_CR39","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1239\/aap\/1183667613","volume":"39","author":"AR Wade","year":"2007","unstructured":"Wade, A.R.: Explicit laws of large numbers for random nearest-neighbour-type graphs. Adv. Appl. Probab. 39(2), 326\u2013342 (2007)","journal-title":"Adv. Appl. Probab."},{"key":"218_CR40","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1002\/j.1538-7305.1965.tb04170.x","volume":"44","author":"AD Wyner","year":"1965","unstructured":"Wyner, A.D.: Capabilities of bounded discrepancy decoding. Bell System Tech. J. 44, 1061\u20131122 (1965)","journal-title":"Bell System Tech. J."},{"issue":"2","key":"218_CR41","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1214\/aoap\/1034968144","volume":"6","author":"Y-C Yao","year":"1996","unstructured":"Yao, Y.-C., Simons, G.: A large-dimensional independent and identically distributed property for nearest neighbor counts in Poisson processes. Ann. Appl. Probab. 6(2), 561\u2013571 (1996)","journal-title":"Ann. Appl. Probab."},{"issue":"7","key":"218_CR42","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.1109\/JSAC.2009.090904","volume":"27","author":"CW Yu","year":"2009","unstructured":"Yu, C.W.: Computing subgraph probability of random geometric graphs with applications in quantitative analysis of ad hoc networks. IEEE J. Select. Areas Commun. 27(7), 1056\u20131065 (2009)","journal-title":"IEEE J. Select. Areas Commun."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00218-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00218-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00218-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T10:00:35Z","timestamp":1723197635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00218-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,6]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["218"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00218-8","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2020,7,6]]},"assertion":[{"value":"10 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}