{"id":898,"date":"2024-02-24T13:11:36","date_gmt":"2024-02-24T13:11:36","guid":{"rendered":"https:\/\/serhatdiker.com\/?p=898"},"modified":"2025-05-10T10:50:31","modified_gmt":"2025-05-10T10:50:31","slug":"rassal-aglar-erdos-renyi-rassal-ag-modeli","status":"publish","type":"post","link":"https:\/\/serhatdiker.com\/index.php\/2024\/02\/24\/rassal-aglar-erdos-renyi-rassal-ag-modeli\/","title":{"rendered":"Rassal A\u011flar &#038; Erd\u00f6s-Renyi Rassal A\u011f Modeli"},"content":{"rendered":"<style>\/*! elementor - v3.19.0 - 07-02-2024 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style>\n<h2>Rassal A\u011flar<\/h2>\n<p>Rassal a\u011flar, a\u011f teorisinin bir dal\u0131 olarak, d\u00fc\u011f\u00fcmler (noktalar) ve aralar\u0131ndaki kenarlar (ba\u011flant\u0131lar) taraf\u0131ndan olu\u015fturulan karma\u015f\u0131k yap\u0131lar\u0131 inceleyen bir aland\u0131r. Bu a\u011flar, d\u00fc\u011f\u00fcmler ve kenarlar aras\u0131ndaki ba\u011flant\u0131lar\u0131n rastgele olu\u015ftu\u011fu modeller \u00fczerine kuruludur. Rassal a\u011flar\u0131n temel \u00f6zellikleri ve teorik y\u00f6nleri \u015fu \u015fekildedir:<\/p>\n<p><strong>Tan\u0131m ve Temel Kavramlar<\/strong><\/p>\n<p>Rassal a\u011f, d\u00fc\u011f\u00fcmler aras\u0131ndaki ba\u011flant\u0131lar\u0131n rastgele olu\u015fturuldu\u011fu bir grafik yap\u0131s\u0131n\u0131 ifade eder. Bu yap\u0131lar, bir\u00e7ok ger\u00e7ek d\u00fcnya sisteminin, \u00f6rne\u011fin sosyal a\u011flar\u0131n, biyolojik a\u011flar\u0131n veya ileti\u015fim a\u011flar\u0131n\u0131n soyut temsilleri olarak kullan\u0131l\u0131r.<\/p>\n<p><strong>Model Tipleri<\/strong><\/p>\n<p>Rassal a\u011flar, farkl\u0131 modellerle temsil edilebilir. En bilinen rassal a\u011f modellerinden biri Erd\u00f6s-R\u00e9nyi modelidir. Bu modelde, her d\u00fc\u011f\u00fcm \u00e7ifti aras\u0131nda sabit bir olas\u0131l\u0131kla ba\u011flant\u0131 olu\u015fturulur. Ba\u015fka bir pop\u00fcler model, Barab\u00e1si-Albert modelidir, bu model tercihli ba\u011flanma prensibiyle b\u00fcy\u00fcyen a\u011flar\u0131 temsil eder.<\/p>\n<p><strong>Derece Da\u011f\u0131l\u0131m\u0131<\/strong><\/p>\n<p>Rassal a\u011flarda, d\u00fc\u011f\u00fcmlerin derecesi (bir d\u00fc\u011f\u00fcm\u00fcn ba\u011flant\u0131 say\u0131s\u0131) \u00f6nemli bir \u00f6zelliktir. Erd\u00f6s-R\u00e9nyi modelinde, derece da\u011f\u0131l\u0131m\u0131 genellikle *Poisson da\u011f\u0131l\u0131m\u0131na uyar. Di\u011fer modellerde, \u00f6zellikle tercihli ba\u011flanma ile b\u00fcy\u00fcyen a\u011flarda, derece da\u011f\u0131l\u0131m\u0131 genellikle bir g\u00fc\u00e7 yasas\u0131n\u0131 takip eder.<\/p>\n<p>*Poisson da\u011f\u0131l\u0131m\u0131, olas\u0131l\u0131k kuram\u0131 ve istatistik bilim kollar\u0131nda bir ayr\u0131k olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131 olup belli bir sabit zaman birim aral\u0131\u011f\u0131nda meydana gelme say\u0131s\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 ifade eder. Bu zaman aral\u0131\u011f\u0131nda ortalama olay meydana gelme say\u0131s\u0131n\u0131n bilindi\u011fi ve herhangi bir olayla onu hemen takip eden olay aras\u0131ndaki zaman fark\u0131n\u0131n, \u00f6nceki zaman farklar\u0131ndan ba\u011f\u0131ms\u0131z olu\u015ftu\u011fu kabul edilir. (Vikipedi)<\/p>\n<p><strong>K\u00fcmeleme Katsay\u0131s\u0131 ve A\u011f Yap\u0131s\u0131<\/strong><\/p>\n<p>Rassal a\u011flarda k\u00fcmeleme katsay\u0131s\u0131, bir d\u00fc\u011f\u00fcm\u00fcn kom\u015fular\u0131n\u0131n birbirine ne kadar s\u0131k ba\u011fland\u0131\u011f\u0131n\u0131 g\u00f6sterir. Erd\u00f6s-R\u00e9nyi gibi baz\u0131 rassal a\u011f modellerinde, k\u00fcmeleme katsay\u0131s\u0131 genellikle d\u00fc\u015f\u00fckt\u00fcr.<\/p>\n<p><strong>Yol Uzunluklar\u0131 ve K\u00fc\u00e7\u00fck D\u00fcnya Fenomeni<\/strong><\/p>\n<p>Rassal a\u011flarda, d\u00fc\u011f\u00fcmler aras\u0131 ortalama en k\u0131sa yol uzunlu\u011fu s\u0131kl\u0131kla incelenir. Baz\u0131 rassal a\u011flar, &#8220;k\u00fc\u00e7\u00fck d\u00fcnya&#8221; \u00f6zelli\u011fine sahiptir, yani d\u00fc\u011f\u00fcmler aras\u0131ndaki ortalama mesafe, a\u011f\u0131n b\u00fcy\u00fckl\u00fc\u011f\u00fcne k\u0131yasla olduk\u00e7a k\u00fc\u00e7\u00fckt\u00fcr.<\/p>\n<p><strong>Dev Bile\u015fen ve A\u011f Ba\u011flant\u0131l\u0131l\u0131\u011f\u0131<\/strong><\/p>\n<p>Bir rassal a\u011fda, belirli bir ba\u011flant\u0131 olas\u0131l\u0131\u011f\u0131ndan sonra, a\u011f\u0131n b\u00fcy\u00fck bir k\u0131sm\u0131n\u0131 kapsayan bir dev bile\u015fenin ortaya \u00e7\u0131kt\u0131\u011f\u0131 g\u00f6zlemlenir. Bu, a\u011f\u0131n ba\u011flant\u0131l\u0131l\u0131\u011f\u0131 ile ilgili \u00f6nemli bir \u00f6zelliktir.<\/p>\n<p><strong>Matematiksel ve \u0130statistiksel Analizler<\/strong><\/p>\n<p>Rassal a\u011flar\u0131n analizi genellikle olas\u0131l\u0131k teorisi ve istatistiksel metodlar kullan\u0131larak yap\u0131l\u0131r. Bu analizler, a\u011f\u0131n yap\u0131sal \u00f6zelliklerini ve davran\u0131\u015f\u0131n\u0131 anlamak i\u00e7in \u00f6nemlidir.<\/p>\n<p><strong>Uygulamalar ve Ger\u00e7ek D\u00fcnya Ba\u011flant\u0131lar\u0131<\/strong><\/p>\n<p>Rassal a\u011f modelleri, ger\u00e7ek d\u00fcnya a\u011flar\u0131n\u0131n \u00f6zelliklerini anlamak ve tahmin etmek i\u00e7in kullan\u0131l\u0131r. Bu modeller, epidemiyoloji, sosyoloji, bilgisayar bilimi ve biyoloji gibi bir\u00e7ok alanda uygulanabilir.<\/p>\n<h2>Erd\u00f6s-Renyi Rassal A\u011f Modeli<\/h2>\n<p>Erd\u00f6s-Renyi Rassal A\u011f Modeli (ER Modeli), rastgele graf teorisi kapsam\u0131nda \u00f6nemli bir yer tutan bir modeldir. Bu model, Paul Erd\u00f6s ve Alfred R\u00e9nyi taraf\u0131ndan 1959 y\u0131l\u0131nda tan\u0131t\u0131lm\u0131\u015ft\u0131r ve a\u011f teorisindeki en temel modellerden biridir. Modelin temel \u00f6zelli\u011fi, graflar\u0131n rastgele olu\u015fturulmas\u0131d\u0131r. \u015eimdi bu modeli detayl\u0131 bir \u015fekilde anlatal\u0131m:<\/p>\n<p><strong>Modelin Tan\u0131m\u0131<\/strong><\/p>\n<p>Erd\u00f6s-Renyi modeli, d\u00fc\u011f\u00fcmler aras\u0131ndaki ba\u011flant\u0131lar\u0131n rastgele olu\u015fturuldu\u011fu bir a\u011f modelidir. Bu modelde, her d\u00fc\u011f\u00fcm \u00e7ifti aras\u0131nda ba\u011flant\u0131 olu\u015fturma olas\u0131l\u0131\u011f\u0131 sabittir ve bu olas\u0131l\u0131k t\u00fcm d\u00fc\u011f\u00fcm \u00e7iftleri i\u00e7in ayn\u0131d\u0131r.<\/p>\n<p><strong>D\u00fc\u011f\u00fcm ve Kenarlar<\/strong><\/p>\n<p>Modelde, N say\u0131da d\u00fc\u011f\u00fcm bulunur. Her bir d\u00fc\u011f\u00fcm \u00e7ifti aras\u0131nda, \u00f6nceden belirlenmi\u015f bir p olas\u0131l\u0131\u011f\u0131 ile kenar (ba\u011flant\u0131) olu\u015fturulur. Bu i\u015flem, t\u00fcm d\u00fc\u011f\u00fcm \u00e7iftleri i\u00e7in ba\u011f\u0131ms\u0131z olarak ger\u00e7ekle\u015ftirilir.<\/p>\n<p><strong>Graflar\u0131n Olu\u015fumu<\/strong><\/p>\n<p>Bir Erd\u00f6s-Renyi grafi\u011fi olu\u015fturmak i\u00e7in, ba\u015flang\u0131\u00e7ta N d\u00fc\u011f\u00fcm\u00fc olan ve aralar\u0131nda hi\u00e7 kenar olmayan bir a\u011f al\u0131n\u0131r. Daha sonra, her d\u00fc\u011f\u00fcm \u00e7ifti i\u00e7in, p olas\u0131l\u0131\u011f\u0131 ile bir kenar eklenir ya da eklenmez.<\/p>\n<p><strong>Parametreler<\/strong><\/p>\n<p>Bu modelde iki temel parametre vard\u0131r: N (d\u00fc\u011f\u00fcm say\u0131s\u0131) ve p (kenar olu\u015fturma olas\u0131l\u0131\u011f\u0131). N&#8217;nin b\u00fcy\u00fck, p&#8217;nin k\u00fc\u00e7\u00fck oldu\u011fu durumlarda, a\u011f seyrek (sparse) bir yap\u0131ya sahip olur.<\/p>\n<p><strong>Ba\u011flant\u0131lar\u0131n Da\u011f\u0131l\u0131m\u0131<\/strong><\/p>\n<p>Erd\u00f6s-Renyi modelinde, d\u00fc\u011f\u00fcmlerin dereceleri (yani ka\u00e7 tane kenara sahip olduklar\u0131) genellikle Poisson da\u011f\u0131l\u0131m\u0131na uyar. Bu, \u00e7o\u011fu d\u00fc\u011f\u00fcm\u00fcn yakla\u015f\u0131k olarak ortalama derecede ba\u011flant\u0131ya sahip oldu\u011fu anlam\u0131na gelir.<\/p>\n<p><strong>Dev Bile\u015fenin Olu\u015fumu<\/strong><\/p>\n<p>Erd\u00f6s-Renyi modelinde, belirli bir p de\u011feri (kritik e\u015fik) \u00fczerinde, a\u011f\u0131n b\u00fcy\u00fck bir k\u0131sm\u0131n\u0131 kaplayan bir &#8216;dev bile\u015fen&#8217; olu\u015fur. Bu dev bile\u015fen, a\u011fdaki \u00e7o\u011fu d\u00fc\u011f\u00fcm\u00fcn birbiriyle dolayl\u0131 olarak ba\u011flant\u0131l\u0131 oldu\u011fu b\u00fcy\u00fck bir alt grafd\u0131r.<\/p>\n<p><strong>K\u00fcmeleme Katsay\u0131s\u0131<\/strong><\/p>\n<p>Erd\u00f6s-Renyi modelinde, k\u00fcmeleme katsay\u0131s\u0131 genellikle d\u00fc\u015f\u00fckt\u00fcr. Bu, d\u00fc\u011f\u00fcmlerin kom\u015fular\u0131n\u0131n birbiriyle ba\u011flant\u0131l\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131n d\u00fc\u015f\u00fck oldu\u011fu anlam\u0131na gelir.<\/p>\n<p><strong>Yol Uzunlu\u011fu<\/strong><\/p>\n<p>A\u011f\u0131n ortalama yol uzunlu\u011fu, genellikle log(N)\/log(ortalama derece) ile orant\u0131l\u0131d\u0131r. Bu, d\u00fc\u011f\u00fcmler aras\u0131ndaki ortalama mesafenin a\u011f\u0131n b\u00fcy\u00fckl\u00fc\u011f\u00fc ile logaritmik olarak artt\u0131\u011f\u0131 anlam\u0131na gelir.<\/p>\n<p><strong>Ba\u011flant\u0131s\u0131zl\u0131k<\/strong><\/p>\n<p>p \u00e7ok d\u00fc\u015f\u00fckse, a\u011f b\u00fcy\u00fck oranda ba\u011flant\u0131s\u0131z par\u00e7alardan olu\u015fur. Her d\u00fc\u011f\u00fcm, yaln\u0131zca birka\u00e7 di\u011fer d\u00fc\u011f\u00fcm ile ba\u011flant\u0131l\u0131d\u0131r ve geni\u015f \u00f6l\u00e7ekli ba\u011flant\u0131lar yoktur.<\/p>\n<p><strong>Kritik E\u015fikler<\/strong><\/p>\n<p>Erd\u00f6s-Renyi modelinde, belirli kritik e\u015fikler vard\u0131r. Bu e\u015fiklerin alt\u0131nda a\u011f par\u00e7al\u0131, \u00fcst\u00fcnde ise birle\u015fik bir yap\u0131dad\u0131r. Bu e\u015fik de\u011feri, genellikle 1\/N civar\u0131ndad\u0131r.<\/p>\n<h2>Erd\u00f6s-Renyi Makale \u0130ncelemeleri<\/h2>\n<ol style=\"margin-top: 0cm;\" start=\"1\" type=\"1\">\n<li>A study on properties of random interval graphs and Erd\u0151s R\u00e9nyi graph g(n, 2\/3) &#8211; Iliopoulos, V. &#8211; Journal of Discrete Mathematical Sciences and Cryptography, 20(8), pp. 1697\u20131720 \u2013 2017\n<\/li>\n<li>On random walks and random sampling to find max degree nodes in assortative erdos renyi graphs &#8211; \u00a0\u00a0\u00a0\u00a0 Stokes, J., Weber, S. &#8211; 2016 IEEE Global Communications Conference, GLOBECOM 2016 &#8211; Proceedings, 7842044 \u2013 2016\n<\/li>\n<li>Numerical simulations of the phase transition property of the explosive percolation model on Erd\u00f6s R\u00e9nyi random network &#8211; Li, Y., Tang, G., Song, L.-J., &#8230;Xia, H., Hao, D.-P. &#8211; Wuli Xuebao\/Acta Physica Sinica, 62(4), 046401 &#8211; 2013<\/li>\n<\/ol>\n<p><strong>Makale 1) A study on properties of random interval graphs and Erd\u0151s R\u00e9nyi graph g(n, 2\/3)<\/strong><\/p>\n<p>Makale, rastgele aral\u0131k grafikleri ve Erd\u0151s-R\u00e9nyi graf G(n,2\/3) \u00fczerindeki \u00e7al\u0131\u015fmalar\u0131 detayl\u0131 bir \u015fekilde inceliyor. Ana odak, bu graf t\u00fcrlerinin kenar say\u0131lar\u0131 ve d\u00fc\u011f\u00fcm derecelerinin da\u011f\u0131l\u0131m\u0131 gibi \u00f6zelliklerinin tahmin edilmesi \u00fczerinedir. Yazar, rastgele aral\u0131k grafiklerinde kenar say\u0131s\u0131n\u0131n n^(2\/3) civar\u0131nda oldu\u011funu ve d\u00fc\u011f\u00fcm derecelerinin Erd\u0151s-R\u00e9nyi modeline g\u00f6re \u00e7ok daha geni\u015f bir aral\u0131kta da\u011f\u0131ld\u0131\u011f\u0131n\u0131 belirtiyor. Ayr\u0131ca, rastgele aral\u0131k grafiklerinde d\u00fc\u011f\u00fcm derecelerinin Erd\u0151s-R\u00e9nyi modeline k\u0131yasla daha da\u011f\u0131t\u0131k oldu\u011fu ve baz\u0131 durumlarda maksimum derecenin n\u22121 oldu\u011fu g\u00f6steriliyor. Bu sonu\u00e7lar, rastgele grafik teorisinde \u00f6nemli bir katk\u0131 sa\u011fl\u0131yor ve bu graf t\u00fcrlerinin yap\u0131sal \u00f6zelliklerine dair daha derin anlay\u0131\u015flar sunuyor.<\/p>\n<p><strong>Makale 2) On random walks and random sampling to find max degree nodes in assortative erdos renyi graphs<\/strong><\/p>\n<p>Makale, Erd\u0151s-R\u00e9nyi grafiklerinde maksimum derece d\u00fc\u011f\u00fcmleri bulmak i\u00e7in rastgele y\u00fcr\u00fcy\u00fc\u015fler ve rastgele \u00f6rnekleme y\u00f6ntemlerini inceliyor. Ara\u015ft\u0131rmada, bu grafiklerde maksimum derece d\u00fc\u011f\u00fcmlerinin say\u0131s\u0131 ve bunlar\u0131 bulmak i\u00e7in en etkili y\u00f6ntemin ne oldu\u011fu sorular\u0131 ele al\u0131n\u0131yor. Makalede, b\u00fcy\u00fck Erd\u0151s-R\u00e9nyi grafiklerinde ortalama olarak tek bir maksimum derece d\u00fc\u011f\u00fcm\u00fc oldu\u011fu ve rastgele y\u00fcr\u00fcy\u00fc\u015f ile rastgele \u00f6rnekleme y\u00f6ntemlerinin performans\u0131n\u0131n grafi\u011fin d\u00fczenlili\u011fine (assortativity) ba\u011fl\u0131 oldu\u011fu sonu\u00e7lar\u0131na var\u0131l\u0131yor. Ayr\u0131ca, rastgele y\u00fcr\u00fcy\u00fc\u015f y\u00f6nteminin y\u00fcksek d\u00fczenli grafiklerde daha etkili oldu\u011fu g\u00f6steriliyor. Bu bulgular, sosyal a\u011flarda pop\u00fcler kullan\u0131c\u0131lar\u0131 veya \u00f6nemli d\u00fc\u011f\u00fcmleri bulma konusunda faydal\u0131 olabilir.<\/p>\n<p><strong>Makale 3) Numerical simulations of the phase transition property of the explosive percolation model on Erd\u00f6s R\u00e9nyi random network<\/strong><\/p>\n<p>Bu makale, Erd\u0151s-R\u00e9nyi rastgele a\u011flar\u0131nda patlay\u0131c\u0131 perkolasyon modelinin faz ge\u00e7i\u015f \u00f6zelliklerine y\u00f6nelik say\u0131sal sim\u00fclasyonlar\u0131 inceliyor. \u00c7al\u0131\u015fma, Achlioptas s\u00fcreci taraf\u0131ndan tetiklenen patlay\u0131c\u0131 perkolasyon modelinin Erd\u0151s-R\u00e9nyi rastgele a\u011flar \u00fczerindeki faz ge\u00e7i\u015f \u00f6zelliklerini, d\u00fczen parametresi, ortalama k\u00fcmelenme boyutu, anlar, standart sapma ve k\u00fcmelenme heterojenli\u011fi gibi temel perkolasyon niceliklerini say\u0131sal sim\u00fclasyonlarla analiz ediyor. Sonu\u00e7 olarak, bu niceliklerin hepsi, perkolasyon e\u015fi\u011finde s\u00fcrekli faz ge\u00e7i\u015flerinin tipik bir \u00f6zelli\u011fi olan g\u00fc\u00e7 yasas\u0131 \u00f6l\u00e7eklenme davran\u0131\u015f\u0131n\u0131 sergiliyor, ancak d\u00fczen parametresi ayn\u0131 anda kesikli bir ge\u00e7i\u015f \u00f6zelli\u011fi g\u00f6steriyor. Bu nedenle, Erd\u0151s-R\u00e9nyi rastgele a\u011flar\u0131ndaki patlay\u0131c\u0131 perkolasyon ge\u00e7i\u015fi ne standart bir kesikli faz ge\u00e7i\u015fi ne de d\u00fczenli rastgele perkolasyon modelindeki s\u00fcrekli ge\u00e7i\u015f olarak kabul edilebilir. Bu, perkolasyon modelinin kendine \u00f6zg\u00fc bir &#8220;tekil&#8221; faz ge\u00e7i\u015fi oldu\u011funu g\u00f6stermektedir.<\/p>\n<p><strong>Kaynak\u00e7a<\/strong><\/p>\n<ol>\n<li>Kun, J. (2013). The Erd\u0151s-R\u00e9nyi Random Graph. Retrieved from <a href=\"https:\/\/jeremykun.com\/2013\/08\/22\/the-erdos-renyi-random-graph\/\">Jeremy <\/a><a href=\"https:\/\/jeremykun.com\/2013\/08\/22\/the-erdos-renyi-random-graph\/\">Kun&#8217;s<\/a><a href=\"https:\/\/jeremykun.com\/2013\/08\/22\/the-erdos-renyi-random-graph\/\"> Blog<\/a>.<\/li>\n<li>Li Yan, Tang Gang, Song Li-Jiang, Xun Zhi-Peng, Xia Hui, Hao Da-Peng. (2013). Numerical simulations of the phase transition property of the explosive percolation model on Erd\u00f6s R\u00e9nyi random network. Acta Physica Sinica, 62(4). DOI: <a href=\"https:\/\/wulixb.iphy.ac.cn\/article\/doi\/10.7498\/aps.62.046401\">10.7498\/aps.62.046401<\/a>.<\/li>\n<li>Iliopoulos, V. (2016). A study on properties of random interval graphs and Erd\u0151s R\u00e9nyi graph \ud835\udca2(n, 2\/3). Journal of Discrete Mathematical Sciences &amp; Cryptography. DOI: <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/09720529.2016.1184453\">10.1080\/09720529.2016.1184453<\/a>.<\/li>\n<li>Stokes, J., Weber, S. (2016). On random walks and random sampling to find max degree nodes in assortative erdos renyi graphs . IEEE Xplore. DOI: <a href=\"https:\/\/ieeexplore.ieee.org\/document\/7842044\">10.1109\/XXX.2016.7842044<\/a>.<\/li>\n<li>Scopus Database. Retrieved from <a href=\"https:\/\/www.scopus.com\/\">Scopus<\/a>.<\/li>\n<li>Python Igraph Tutorial on Erd\u0151s-R\u00e9nyi Graphs. Retrieved from <a href=\"https:\/\/python.igraph.org\/en\/latest\/tutorials\/erdos_renyi.html\">Python <\/a><a href=\"https:\/\/python.igraph.org\/en\/latest\/tutorials\/erdos_renyi.html\">Igraph<\/a> <a href=\"https:\/\/python.igraph.org\/en\/latest\/tutorials\/erdos_renyi.html\">Documentation<\/a>.<\/li>\n<li>Wikipedia. Poisson Da\u011f\u0131l\u0131m\u0131. Retrieved from <a href=\"https:\/\/tr.wikipedia.org\/wiki\/Poisson_da%C4%9F%C4%B1l%C4%B1m%C4%B1\">Turkish<\/a><a href=\"https:\/\/tr.wikipedia.org\/wiki\/Poisson_da%C4%9F%C4%B1l%C4%B1m%C4%B1\"> Wikipedia<\/a>.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Rassal A\u011flar Rassal a\u011flar, a\u011f teorisinin bir dal\u0131 olarak, d\u00fc\u011f\u00fcmler (noktalar) ve aralar\u0131ndaki kenarlar (ba\u011flant\u0131lar) taraf\u0131ndan olu\u015fturulan karma\u015f\u0131k yap\u0131lar\u0131 inceleyen bir aland\u0131r. Bu a\u011flar, d\u00fc\u011f\u00fcmler ve&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":982,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[162,48,160,167,173,172,164,157,175,166,180,168,177,170,178,163,179,165,169,176,161,159,174,156,158,40,171,31],"class_list":["post-898","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-veri-bilimi","tag-ag-kumelenmesi","tag-ag-teorisi","tag-ag-yapisi","tag-average-path-length","tag-baglanti-olasiligi","tag-biyolojik-aglar","tag-dev-bilesen","tag-erdos-renyi-modeli","tag-graph-centrality","tag-graph-clustering","tag-graph-connectivity","tag-graph-diameter","tag-graph-metrics","tag-graph-modeling","tag-igraph-erdos-renyi","tag-kucuk-dunya-fenomeni","tag-modulerlik","tag-network-topology","tag-percolation-theory","tag-phase-transition","tag-poisson-dagilimi","tag-random-graph","tag-random-walks","tag-rassal-aglar","tag-rastgele-ag","tag-sosyal-ag-analizi","tag-sosyal-bilimlerde-ag","tag-veri-bilimi"],"_links":{"self":[{"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/posts\/898","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/comments?post=898"}],"version-history":[{"count":4,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/posts\/898\/revisions"}],"predecessor-version":[{"id":903,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/posts\/898\/revisions\/903"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/media\/982"}],"wp:attachment":[{"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/media?parent=898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/categories?post=898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/serhatdiker.com\/index.php\/wp-json\/wp\/v2\/tags?post=898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}