{"id":249,"date":"2026-01-20T03:23:14","date_gmt":"2026-01-20T03:23:14","guid":{"rendered":"https:\/\/mrc-baku.org\/?p=249"},"modified":"2026-05-01T03:28:11","modified_gmt":"2026-05-01T03:28:11","slug":"general-seminar-by-turker-biyikoglu-2","status":"publish","type":"post","link":"https:\/\/mrc-baku.org\/index.php\/general-seminar-by-turker-biyikoglu-2\/","title":{"rendered":"General Seminar by Turker Biyikoglu"},"content":{"rendered":"\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n<meta charset=\"UTF-8\">\n<meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n<title>Seminar Announcement \u2014 Mathematics Research Center<\/title>\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,600;1,400;1,500&#038;family=DM+Mono:wght@300;400;500&#038;family=Outfit:wght@300;400;500;600&#038;display=swap\" rel=\"stylesheet\">\n<script>MathJax = { tex: { inlineMath: [['\\\\(','\\\\)']] } };<\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-chtml.js\" async><\/script>\n<style>\n  body { background: #eee; padding: 2rem; margin: 0; }\n<\/style>\n<\/head>\n<body>\n\n<!--\n  \u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n  WORDPRESS BLOCK PATTERN \u2014 Seminar Announcement\n  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  USAGE:\n  \u2022 Paste the <style> block ONCE on your site (via WPCode or\n    theme header) \u2014 skip if already present from other blocks.\n  \u2022 For each announcement, paste one .ann-block into its own\n    Custom HTML block.\n  \u2022 Update: seminar type badge, date\/time\/location, title,\n    speaker name, affiliation, abstract, and logo URL.\n  \u2022 Change data-type on .ann-block to switch badge colour:\n      data-type=\"general\"   \u2192 slate\n      data-type=\"research\"  \u2192 rust\n      data-type=\"student\"   \u2192 gold\n  \u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n-->\n\n<!-- \u2500\u2500\u2500 STYLE BLOCK \u2014 paste once \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 -->\n<style>\n:root {\n  --cream:    #F5F0E8;\n  --ink:      #1A1610;\n  --rust:     #B84A2F;\n  --gold:     #C99A2E;\n  --slate:    #3D4A5C;\n  --mist:     #E8EDF4;\n  --rule:     #C8BFA8;\n  --garamond: 'EB Garamond', Georgia, serif;\n  --mono:     'DM Mono', monospace;\n  --sans:     'Outfit', sans-serif;\n}\n*, *::before, *::after { box-sizing: border-box; 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A major theme in complex networks is to understand the relations between network descriptors and their connection to the networks\u2019 function. This is a daunting task because of a large number of quantitative measures and each one typically capturing only a particular aspect of the network. <\/p> <p>\nThe aim of this talk is to rigorously connect several network descriptors and concepts using mathematical tools.<\/p> <p>\nThe central notion of our talk is entropy. Entropy plays a fundamental role in many areas of the physical sciences in quantifying disorder and complexity. Entropy is also a particularly relevant notion for studying complex systems and networks. Entropy is also closely related to the spectral radius (largest eigenvalue) of the graphs\u2019 adjacency matrix. Another central player of our talk, which at first sight seems unrelated to the concept of entropy, is the so-called Randi\u0107 index, introduced in the 1970s to study chemical compounds. We will see that the topological entropy is bounded from below by the Randi\u0107 index. Finally, the Randi\u0107 index brings us back to real-world networks. In social networks vertices with high degree are often adjacent to other high-degree vertices, a tendency referred to as assortative mixing or assortativity. We will see that Randi\u0107 index and assortativity come to the same thing in different areas. <\/p> <p>\nWe finish our talk with a fundamental hierarchical structure from computer science so-called breadth-first search ordering with decreasing degrees that characterized maximization of all these notions. <\/p> <p>\nThis is a joint work with Fatihcan Atay, Bilkent University, Ankara.<\/p>\n    <\/div>\n  <\/div>\n\n  <!-- Footer -->\n  <div class=\"ann-footer\">\n    <span>Mathematics Research Center \u00b7 ASOIU, Baku<\/span>\n    <a href=\"\/seminars\/\">All seminars \u2192<\/a>\n  <\/div>\n\n<\/div><!-- \/.ann-block -->\n<!-- \u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n     END SEMINAR ANNOUNCEMENT\n     \u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 -->\n\n\n<!-- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     BLANK TEMPLATE \u2014 copy this for new announcements\n     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 -->\n<!--\n\n<div class=\"ann-block\" data-type=\"general\">\n\n  <div class=\"ann-topbar\"><\/div>\n\n  <div class=\"ann-logo-row\">\n    <img decoding=\"async\" class=\"ann-logo\" src=\"LOGO_URL_HERE\" alt=\"ASOIU Mathematics Research Center\">\n  <\/div>\n\n  <div class=\"ann-poster\">\n    <div class=\"ann-type\">General Seminar<\/div>\n    <div class=\"ann-poster-rule\"><\/div>\n    <div class=\"ann-title\">\n      TALK TITLE HERE\n    <\/div>\n    <div class=\"ann-speaker\">Speaker Name<\/div>\n    <div class=\"ann-affil\">Institution<\/div>\n  <\/div>\n\n  <div class=\"ann-meta\">\n    <div class=\"ann-meta-item\">\n      <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M7 0H2a1 1 0 00-1 1v2h14V1a1 1 0 00-1-1H7zm7 4H1v10a1 1 0 001 1h12a1 1 0 001-1V4z\"\/><\/svg>\n      <span><span class=\"ann-meta-label\">Date&nbsp;<\/span>Month DD, YYYY<\/span>\n    <\/div>\n    <div class=\"ann-meta-item\">\n      <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 1a5 5 0 100 10A5 5 0 008 1zM0 8a8 8 0 1116 0A8 8 0 010 8z\"\/><path d=\"M7.5 4.5v4l2.5 1.5.5-.87L8.5 8V4.5z\"\/><\/svg>\n      <span><span class=\"ann-meta-label\">Time&nbsp;<\/span>HH:MM<\/span>\n    <\/div>\n    <div class=\"ann-meta-item\">\n      <svg viewBox=\"0 0 16 16\" fill=\"currentColor\"><path d=\"M8 0C5.24 0 3 2.24 3 5c0 3.75 5 11 5 11s5-7.25 5-11c0-2.76-2.24-5-5-5zm0 7.5a2.5 2.5 0 110-5 2.5 2.5 0 010 5z\"\/><\/svg>\n      <span><span class=\"ann-meta-label\">Location&nbsp;<\/span>Room \/ Online<\/span>\n    <\/div>\n  <\/div>\n\n  <div class=\"ann-abstract\">\n    <div class=\"ann-abstract-label\">Abstract<\/div>\n    <div class=\"ann-abstract-body\">\n      <p>Abstract text here. Use \\(...\\) for inline math.<\/p>\n    <\/div>\n  <\/div>\n\n  <div class=\"ann-footer\">\n    <span>Mathematics Research Center \u00b7 ASOIU, Baku<\/span>\n    <a href=\"\/seminars\/\">All seminars \u2192<\/a>\n  <\/div>\n\n<\/div>\n\n-->\n\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Seminar Announcement \u2014 Mathematics Research Center General Seminar Graph Entropy, Degree Assortativity, and Hierarchical Structures in Networks T\u00fcrker B\u0131y\u0131ko\u011flu ~Mathematics Research Center, ASOIU Date&nbsp;October 9, 2025 Time&nbsp;14:00 Location&nbsp;MRC @ UFAZ 101 Abstract There are various network descriptors for the understanding of complex networks. A major theme in complex networks is to understand the relations between [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_edit_lock":["1777606091:1"],"_edit_last":["1"],"_wp_page_template":["default"],"_wp_old_date":["2026-04-17"]},"categories":[6],"tags":[26],"class_list":["post-249","post","type-post","status-publish","format-standard","hentry","category-generalseminar","tag-graph-theory"],"_links":{"self":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts\/249","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/comments?post=249"}],"version-history":[{"count":1,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts\/249\/revisions"}],"predecessor-version":[{"id":250,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/posts\/249\/revisions\/250"}],"wp:attachment":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/media?parent=249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/categories?post=249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/tags?post=249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}