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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Network robustness ： ウィキペディア英語版 Network robustness Network robustness in network science and graph theory is the characteristic of the network to remain connected while its nodes being removed. Robustness comes from availability of alternative paths between two distinct nodes, which makes it possible to connect them in situations of network damage:.〔Dekker, Anthony H., and Bernard D. Colbert. "Network robustness and graph topology." Proceedings of the 27th Australasian conference on Computer science-Volume 26. Australian Computer Society, Inc., 2004.〕 It is understood as the result of network structure, or topology, not processes underlying the network itself. For example, network robustness of power grid is examined by deletion of transformers, but not effecting the properties of the cables or transformers. The concept is used in engineering, defense, finance to secure the relevant networks from collapses. ==Connectedness of the network== Network of N nodes is fully connected if every node is connected to N-1 other nodes. Network is disconnected if there exist two distinct nodes that cannot be connected through other nodes. There are different measures of network connection: * the network diameter ''d'' is the largest minimal degree between two nodes. The lower is the diameter of the network, the better it is connected. Diameter of the fully connected network is 1. * the node connectivity is the smallest number of nodes whose removal results in disconnected network. The node connectivity of the fully connected network of size N is N-1. * the link connectivity is the smallest number of links whose removal results in a disconnected network. The link connectivity of the fully connected network of size N is N-1. The criterion for the network breakdown is the size of the largest cluster after nodes removal. The existence of large cluster can be checked by Molloy-Reed criterion〔Cohen, Reuven, et al. "Resilience of the Internet to random breakdowns." Physical review letters 85.21 (2000): 4626.〕 $\backslash kappa=>2\}$ where $$ and $$ are first and second moment of degree distribution. Critical threshold for the existence of the large cluster is: $f\_c=1--1\}$ Robustness of random and scale-free networks The exact formulation of the breakdown criteria depends on the network topology. The most frequent and the most studied types of real world networks are random and scale-free networks. ==Random network== also known as Erdös-Rényi model, is a model of undirected network with a fixed probability of two nodes to be connected. They are equally tolerant against random and deliberate attacks.〔Albert, Réka, Hawoong Jeong, and Albert-László Barabási. "Error and attack tolerance of complex networks." Nature 406.6794 (2000): 378-382.〕 Molloy-Reed criterion for the random network: $\backslash kappa^=$ The critical thershold: $f\_c=1-\{1\; \backslash over$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Network robustness」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.