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A Survey of Fractal Dimensions of NetworksIntroduction

A Survey of Fractal Dimensions of Networks: Introduction [Consider the network 𝔾=(ℕ,𝔸)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathbb {G}} = ( {\mathbb {N}}, {\mathbb {A}})$$ \end{document} where ℕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {N}$$ \end{document} is the set of nodes connected by the set 𝔸\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {A}$$ \end{document} of arcs. Let N≡|ℕ|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$N \equiv \vert {\mathbb {N}} \vert $$ \end{document} be the number of nodes, and let A≡|𝔸|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$A \equiv \vert {\mathbb {A}} \vert $$ \end{document} be the number of arcs. (We use “≡” to denote a definition.)] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Survey of Fractal Dimensions of NetworksIntroduction

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Publisher
Springer International Publishing
Copyright
© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018
ISBN
978-3-319-90046-9
Pages
1 –6
DOI
10.1007/978-3-319-90047-6_1
Publisher site
See Chapter on Publisher Site

Abstract

[Consider the network 𝔾=(ℕ,𝔸)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathbb {G}} = ( {\mathbb {N}}, {\mathbb {A}})$$ \end{document} where ℕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {N}$$ \end{document} is the set of nodes connected by the set 𝔸\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {A}$$ \end{document} of arcs. Let N≡|ℕ|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$N \equiv \vert {\mathbb {N}} \vert $$ \end{document} be the number of nodes, and let A≡|𝔸|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$A \equiv \vert {\mathbb {A}} \vert $$ \end{document} be the number of arcs. (We use “≡” to denote a definition.)]

Published: May 30, 2018

Keywords: Hausdorff Dimension; Fractal Dimension; Sandbox Method; Maximum Euclidean Distance; Felix Hausdorff

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