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第477行： − An interdependent network is a system of coupled networks where nodes of one or more networks depend on nodes in other networks. Such dependencies are enhanced by the developments in modern technology. Dependencies may lead to cascading failures between the networks and a relatively small failure can lead to a catastrophic breakdown of the system. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. A recent study developed a framework to study the cascading failures in an interdependent networks system.<ref>{{Cite journal|author1=S. V. Buldyrev |author2=R. Parshani |author3=G. Paul |author4=H. E. Stanley |author5=S. Havlin |title = Catastrophic cascade of failures in interdependent networks|journal = Nature |volume = 464 |pages = 1025–28 |year = 2010 | doi=10.1038/nature08932 |issue=7291|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all |bibcode=2010Natur.464.1025B|arxiv = 0907.1182 |pmid=20393559}}</ref><ref>{{cite journal|first=Jianxi |last=Gao|first2= Sergey V.|last2= Buldyrev|first3= Shlomo |last3=Havlin|first4= H. Eugene|last4= Stanley|title=Robustness of a Network of Networks|journal=Phys. Rev. Lett.|year=2011|volume=107|pages=195701|url=http://havlin.biu.ac.il/Publications.php?keyword=Robustness+of+a+Tree-like+Network+of+Interdependent+Networks&year=*&match=all | doi = 10.1103/PhysRevLett.107.195701|bibcode=2011PhRvL.107s5701G|arxiv = 1010.5829|issue=19|pmid=22181627 }}</ref> − '''Multilayer networks''' are networks with multiple kinds of relations. Attempts to model real-world systems as multidimensional networks have been used in various fields such as social network analysis, economics, history, urban and international transport, ecology, − psychology, medicine, biology, commerce, climatology, physics, computational neuroscience, operations management, and finance. − − Network problems that involve finding an optimal way of doing something are studied under the name of [[combinatorial optimization]]. Examples include [[flow network|network flow]], [[shortest path problem]], [[transport problem]], [[transshipment problem]], [[Facility location problem|location problem]], [[Matching (graph theory)|matching problem]], [[assignment problem]], [[packing problem]], [[routing|routing problem]], [[Critical Path Analysis]] and [[PERT]] (Program Evaluation & Review Technique).
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==相依网络==
==相依网络==
相依网络是一个耦合的网络系统，其中一个或多个网络的节点依赖于其他网络中的节点。现代科技的发展增强了这种依赖性。依赖关系可能导致网络之间的相继故障，一个相对较小的故障可能导致系统的灾难性崩溃。网络之间依赖性的重要作用可以通过停电这个例子来展示。最近的一项研究开发了一个框架来研究相互依赖的网络系统中的相继故障。<ref>{{Cite journal|author1=S. V. Buldyrev |author2=R. Parshani |author3=G. Paul |author4=H. E. Stanley |author5=S. Havlin |title = Catastrophic cascade of failures in interdependent networks|journal = Nature |volume = 464 |pages = 1025–28 |year = 2010 | doi=10.1038/nature08932 |issue=7291|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all |bibcode=2010Natur.464.1025B|arxiv = 0907.1182 |pmid=20393559}}</ref><ref>{{cite journal|first=Jianxi |last=Gao|first2= Sergey V.|last2= Buldyrev|first3= Shlomo |last3=Havlin|first4= H. Eugene|last4= Stanley|title=Robustness of a Network of Networks|journal=Phys. Rev. Lett.|year=2011|volume=107|pages=195701|url=http://havlin.biu.ac.il/Publications.php?keyword=Robustness+of+a+Tree-like+Network+of+Interdependent+Networks&year=*&match=all | doi = 10.1103/PhysRevLett.107.195701|bibcode=2011PhRvL.107s5701G|arxiv = 1010.5829|issue=19|pmid=22181627 }}</ref>
相依网络是一个耦合的网络系统，其中一个或多个网络的节点依赖于其他网络中的节点。现代科技的发展增强了这种依赖性。依赖关系可能导致网络之间的相继故障，一个相对较小的故障可能导致系统的灾难性崩溃。网络之间依赖性的重要作用可以通过停电这个例子来展示。最近的一项研究开发了一个框架来研究相互依赖的网络系统中的相继故障。<ref>{{Cite journal|author1=S. V. Buldyrev |author2=R. Parshani |author3=G. Paul |author4=H. E. Stanley |author5=S. Havlin |title = Catastrophic cascade of failures in interdependent networks|journal = Nature |volume = 464 |pages = 1025–28 |year = 2010 | doi=10.1038/nature08932 |issue=7291|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all |bibcode=2010Natur.464.1025B|arxiv = 0907.1182 |pmid=20393559}}</ref><ref>{{cite journal|first=Jianxi |last=Gao|first2= Sergey V.|last2= Buldyrev|first3= Shlomo |last3=Havlin|first4= H. Eugene|last4= Stanley|title=Robustness of a Network of Networks|journal=Phys. Rev. Lett.|year=2011|volume=107|pages=195701|url=http://havlin.biu.ac.il/Publications.php?keyword=Robustness+of+a+Tree-like+Network+of+Interdependent+Networks&year=*&match=all | doi = 10.1103/PhysRevLett.107.195701|bibcode=2011PhRvL.107s5701G|arxiv = 1010.5829|issue=19|pmid=22181627 }}</ref>
==多层网络==
==多层网络==
'''多层网络'''是包含多种关系的网络。已经在多个领域尝试将现实世界系统建模为多维网络，例如社会网络分析、经济学、历史、城市和国际交通、生态学、心理学、医学、生物学、商业、气候学、物理学、计算神经科学、运营管理以及金融。
'''多层网络'''是包含多种关系的网络。已经在多个领域尝试将现实世界系统建模为多维网络，例如社会网络分析、经济学、历史、城市和国际交通、生态学、心理学、医学、生物学、商业、气候学、物理学、计算神经科学、运营管理以及金融。
==网络优化==
==网络优化==
关于寻找某些事情最优解的网络问题属于[[组合优化]]的范畴。例如[[流网络|网络流]]、[[最短路径问题]]、[[运输问题]]、[[转运问题]]、[[设施选址问题|选址问题]]、[[匹配(图论)|匹配问题]]、[[分配问题]]、[[装箱问题]]、[[路由|路由问题]]、[[关键路径分析]]和[[PERT]]（计划评审技术）。
关于寻找某些事情最优解的网络问题属于[[组合优化]]的范畴。例如[[流网络|网络流]]、[[最短路径问题]]、[[运输问题]]、[[转运问题]]、[[设施选址问题|选址问题]]、[[匹配(图论)|匹配问题]]、[[分配问题]]、[[装箱问题]]、[[路由|路由问题]]、[[关键路径分析]]和[[PERT]]（计划评审技术）。