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网络科学 (查看源代码)

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The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. The earliest known paper in this field is the famous [[Seven Bridges of Königsberg]] written by [[Leonhard Euler]] in 1736. Euler's mathematical description of vertices and edges was the foundation of [[graph theory]], a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of [[graph theory]] continued to develop and found applications in chemistry (Sylvester, 1878).

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The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. The earliest known paper in this field is the famous Seven Bridges of Königsberg written by Leonhard Euler in 1736. Euler's mathematical description of vertices and edges was the foundation of graph theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory continued to develop and found applications in chemistry (Sylvester, 1878).

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网络研究作为分析复杂关系数据的一种手段已经出现在不同的学科中。在这个领域已知最早的论文是1736年欧拉（Leonhard Euler）写的著名的柯尼斯堡七桥问题（Seven Bridges of Königsberg）。欧拉对顶点和边的数学描述是[[图论]]的基础，这是一个研究网络结构中成对关系的性质的数学分支。图论的领域继续发展，并在化学中得到应用(Sylvester，1878)。

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网络研究作为分析复杂关系数据的一种手段已经出现在不同的学科中。在这个领域已知最早的论文是1736年欧拉 Leonhard Euler 写的著名的柯尼斯堡七桥问题Seven Bridges of ~~Königsberg。欧拉对顶点和边的数学描述是~~[[图论]]~~的基础，这是一个研究网络结构中成对关系的性质的数学分支。图理论的领域继续发展，并在化学中得到应用~~(Sylvester，1878)。

[[Dénes Kőnig]], a Hungarian mathematician and professor, wrote the first book in Graph Theory, entitled "Theory of finite and infinite graphs", in 1936 <ref>{{cite book|title=Theory of finite and infinite graphs |author=Dénes Kőnig|publisher=Birkhäuser Boston |isbn=978-1-4684-8971-2 |year=1990 |url=https://link.springer.com/content/pdf/10.1007/978-1-4684-8971-2_2.pdf|type=PDF |doi=10.1007/978-1-4684-8971-2 }}</ref>

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~~Dénes Kőnig, a Hungarian mathematician and professor, wrote the first book in Graph Theory, entitled "Theory of finite and infinite graphs", in 1936 [2]~~

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匈牙利数学家兼教授Dénes Kőnig在1936年写了[[图论]]的第一本书《有限图和无限图理论》（''Theory of finite and infinite graphs''）。

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匈牙利数学家兼教授Dénes Kőnig在1936年写了[[图论]]~~的第一本书《有限图和无限图理论》~~''Theory of finite and infinite graphs''。

[[File:Moreno Sociogram 1st Grade.png|thumb|Moreno's sociogram of a 1st grade class.]]In the 1930s [[Jacob Moreno]], a psychologist in the [[Gestalt psychology|Gestalt]] tradition, arrived in the United States. He developed the [[sociogram]] and presented it to the public in April 1933 at a convention of medical scholars. Moreno claimed that "before the advent of sociometry no one knew what the interpersonal structure of a group 'precisely' looked like" (Moreno, 1953). The sociogram was a representation of the social structure of a group of elementary school students. The boys were friends of boys and the girls were friends of girls with the exception of one boy who said he liked a single girl. The feeling was not reciprocated. This network representation of social structure was found so intriguing that it was printed in [[The New York Times]] (April 3, 1933, page 17). The sociogram has found many applications and has grown into the field of [[social network analysis]].

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In the 1930s Jacob Moreno, a psychologist in the Gestalt tradition, arrived in the United States. He developed the sociogram and presented it to the public in April 1933 at a convention of medical scholars. Moreno claimed that "before the advent of sociometry no one knew what the interpersonal structure of a group 'precisely' looked like" (Moreno, 1953). The sociogram was a representation of the social structure of a group of elementary school students. The boys were friends of boys and the girls were friends of girls with the exception of one boy who said he liked a single girl. The feeling was not reciprocated. This network representation of social structure was found so intriguing that it was printed in The New York Times (April 3, 1933, page 17). The sociogram has found many applications and has grown into the field of social network analysis.

20世纪30年代，格式塔传统的心理学家雅各布·莫雷诺Jacob Moreno来到美国。在1933年4月的一次医学学者大会上，他在大会上展示了他制作的[[社网图]] sociogram。莫雷诺声称“在社会计量学出现之前，没有人知道一个群体的人际关系结构‘精确地’看起来像什么”(莫雷诺，1953)。这张社网图展示一群小学生的社会结构。男孩是男孩的朋友，女孩是女孩的朋友，只有一个男孩说他喜欢另一个单身女孩但是没有得到回应。这个网络展示的社会结构非常有趣，也被刊登在《纽约时报》上(1933年4月3日，第17页)。社网图已经有许多的应用场景，并且已经发展成为[[社会网络分析]]social network analysis的一个子领域。

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Probabilistic theory in network science developed as an offshoot of [[graph theory]] with [[Paul Erdős]] and [[Alfréd Rényi]]'s eight famous papers on [[random graphs]]. For [[social networks]] the [[exponential random graph model]] or p* is a notational framework used to represent the probability space of a tie occurring in a [[social network]]. An alternate approach to network probability structures is the [[network probability matrix]], which models the probability of edges occurring in a network, based on the historic presence or absence of the edge in a sample of networks.

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Probabilistic theory in network science developed as an offshoot of graph theory with Paul Erdős and Alfréd Rényi's eight famous papers on random graphs. For social networks the exponential random graph model or p* is a notational framework used to represent the probability space of a tie occurring in a social network. An alternate approach to network probability structures is the network probability matrix, which models the probability of edges occurring in a network, based on the historic presence or absence of the edge in a sample of networks.

20世纪90年代，在Paul Erdős和Alfréd Rényi发表了8篇关于随机图的著名论文之后，网络科学中的概率论 Probabilistic theory 作为图论的一个分支发展起来了。对于[[社交网络]]social network来说，指数随机图模型或p* (是一个记号框架），用来表示在一个社交网络中连边在概率空间发生的概率。网络概率结构的另一种替代表示方法是网络概率矩阵，它根据网络样本中边的历史信息来计算这条边在网络中出现的概率。

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In 1998, [[David Krackhardt]] and [[Kathleen Carley]] introduced the idea of a meta-network with the PCANS Model. They suggest that "all organizations are structured along these three domains, Individuals, Tasks, and Resources". Their paper introduced the concept that networks occur across multiple domains and that they are interrelated. This field has grown into another sub-discipline of network science called [[dynamic network analysis]].

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In 1998, David Krackhardt and Kathleen Carley introduced the idea of a meta-network with the PCANS Model. They suggest that "all organizations are structured along these three domains, Individuals, Tasks, and Resources". Their paper introduced the concept that networks occur across multiple domains and that they are interrelated. This field has grown into another sub-discipline of network science called dynamic network analysis.

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1998年，David Krackhardt和Kathleen Carley提出了用PCANS模型构建元网络meta-network的想法。他们建议所有的组织都通过“个人、任务和资源”来构建。他们的论文介绍了新的网络概念，即网络发生在多个领域的且相互关联。这个领域已经发展也成为网络科学的另一个子学科，叫做[[动态网络分析]]dynamic network analysis。

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More recently other network science efforts have focused on mathematically describing different network topologies. Duncan Watts reconciled empirical data on networks with mathematical representation, describing the [[small-world network]]. [[Albert-László Barabási]] and [[Reka Albert]] developed the [[scale-free network]] which is a loosely defined network topology that contains hub vertices with many connections, that grow in a way to maintain a constant ratio in the number of the connections versus all other nodes. Although many networks, such as the internet, appear to maintain this aspect, other networks have long tailed distributions of nodes that only approximate scale free ratios.

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More recently other network science efforts have focused on mathematically describing different network topologies. Duncan Watts reconciled empirical data on networks with mathematical representation, describing the small-world network. Albert-László Barabási and Reka Albert developed the scale-free network which is a loosely defined network topology that contains hub vertices with many connections, that grow in a way to maintain a constant ratio in the number of the connections versus all other nodes. Although many networks, such as the internet, appear to maintain this aspect, other networks have long tailed distributions of nodes that only approximate scale free ratios.

最近其他网络科学的研究致力于用数学的方式描述不同网络的拓扑结构。[[邓肯·瓦茨]]Duncan Watts 将网络上的经验数据与数学表达相结合，描述了小世界网络。 [[艾伯特-拉斯洛·巴拉巴西 Albert-László Barabási]] 和 [[Reka Albert]]发现了无标度网络，简单说就是包含Hub中心节点（连边数量很多的节点），且连边的数量和节点数量呈现常数比率的增长方式，即一个网络上节点的度（节点所在连边的数量）分布服从幂指数为2和3之间的幂律分布。尽管许多网络，比如互联网，似乎保持了这样的特性，但是其他网络的节点分布表现出长尾特性，仅仅是接近无标度比例。

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[[用户:思无涯咿呀咿呀|思无涯咿呀咿呀]]（[[用户讨论:思无涯咿呀咿呀|讨论]]）Albert-László Barabási and Reka Albert developed the scale-free network which is a loosely defined network topology that contains hub vertices with many connections, that grow in a way to maintain a constant ratio in the number of the connections versus all other nodes. [[用户:思无涯咿呀咿呀|思无涯咿呀咿呀]]（[[用户讨论:思无涯咿呀咿呀|讨论]]）这一段话怎么理解。

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~~===Department of Defense initiatives===~~

=== 国防部倡议 ===

The U.S. military first became interested in [[network-centric warfare]] as an operational concept based on network science in 1996. John A. Parmentola, the U.S. Army Director for Research and Laboratory Management, proposed to the Army’s Board on Science and Technology (BAST) on December 1, 2003 that Network Science become a new Army research area. The BAST, the Division on Engineering and Physical Sciences for the National Research Council (NRC) of the National Academies, serves as a convening authority for the discussion of science and technology issues of importance to the Army and oversees independent Army-related studies conducted by the National Academies. The BAST conducted a study to find out whether identifying and funding a new field of investigation in basic research, Network Science, could help close the gap between what is needed to realize Network-Centric Operations and the current primitive state of fundamental knowledge of networks.

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The U.S. military first became interested in network-centric warfare as an operational concept based on network science in 1996. John A. Parmentola, the U.S. Army Director for Research and Laboratory Management, proposed to the Army’s Board on Science and Technology (BAST) on December 1, 2003 that Network Science become a new Army research area. The BAST, the Division on Engineering and Physical Sciences for the National Research Council (NRC) of the National Academies, serves as a convening authority for the discussion of science and technology issues of importance to the Army and oversees independent Army-related studies conducted by the National Academies. The BAST conducted a study to find out whether identifying and funding a new field of investigation in basic research, Network Science, could help close the gap between what is needed to realize Network-Centric Operations and the current primitive state of fundamental knowledge of networks.

1996年，美国军方第一次对网络中心战感兴趣，将其作为一个基于网络科学的军事概念。 2003年12月1日，美国陆军研究和实验室管理主任 John A. Parmentola 向陆军科学和技术委员会提议，网络科学成为陆军的一个新的研究领域。科学和技术委员会是美国国家学院国家研究委员会工程和物理科学司的下属部门，主要讨论对陆军重要的科学和技术问题，并且监督美国国家学院进行的与陆军相关的独立研究。

科学和技术委员会进行了一项研究，他们想通过确定和资助一个新的研究领域的基础研究：网络科学，希望可以帮助找到网络中心战所必须的知识，从而缩小实现网络中心战与当前网络科学理论基础的差距。

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As a result, the BAST issued the NRC study in 2005 titled Network Science (referenced above) that defined a new field of basic research in Network Science for the Army. Based on the findings and recommendations of that study and the subsequent 2007 NRC report titled Strategy for an Army Center for Network Science, Technology, and Experimentation, Army basic research resources were redirected to initiate a new basic research program in Network Science. To build a new theoretical foundation for complex networks, some of the key Network Science research efforts now ongoing in Army laboratories address:

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As a result, the BAST issued the NRC study in 2005 titled Network Science (referenced above) that defined a new field of basic research in Network Science for the Army. Based on the findings and recommendations of that study and the subsequent 2007 NRC report titled Strategy for an Army Center for Network Science, Technology, and Experimentation, Army basic research resources were redirected to initiate a new basic research program in Network Science. To build a new theoretical foundation for complex networks, some of the key Network Science research efforts now ongoing in Army laboratories address:

因此，科学和技术委员在2005年发布了NRC的研究报告，题为《网络科学定义了美国陆军网络科学基础研究新领域》。基于这项研究的发现和建议，以及随后2007年 NRC 题为基于网络科学、技术和实战的战略研究报告，陆军基础研究资源被重新投入在网络科学的一个新的基础研究项目。为了建立复杂网络的全新的理论基础，美国陆军实验室正在进行的一些关键的网络科学研究工作致力于:

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* 网络化战争network-enabled warfare所需的最佳人类表现

* 生态系统中基于细胞分子层面的网络建模

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As initiated in 2004 by Frederick I. Moxley with support he solicited from David S. Alberts, the Department of Defense helped to establish the first Network Science Center in conjunction with the U.S. Army at the United States Military Academy (USMA). Under the tutelage of Dr. Moxley and the faculty of the USMA, the first interdisciplinary undergraduate courses in Network Science were taught to cadets at West Point. In order to better instill the tenets of network science among its cadre of future leaders, the USMA has also instituted a five-course undergraduate minor in Network Science.

正如2004年 David S. Alberts支持Frederick I. Moxley那样，国防部帮助美国陆军一起在美国军事学院(USMA)建立了第一个网络科学中心。在Moxley博士和美国军事学院(USMA)研究员的指导下，西点军校开设了首个网络科学本科生课程。为了更好地向其未来领导干部灌输网络科学的信条，美国军事学院还在网络科学下设置了一个5节课本科生辅修课程。

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2006年，美国陆军和英国成立了网络和信息科学国际技术联盟，这是美国陆军研究实验室、英国国防部以及美国和英国的工业和大学联盟之间的合作伙伴关系。该联盟的目标是进行基础研究，以支持两国需要的网络中心作战。

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In 2009, the U.S. Army formed the [[Network Science CTA]], a collaborative research alliance among the [[Army Research Laboratory]], [[CERDEC]], and a consortium of about 30 industrial R&D labs and universities in the U.S. The goal of the alliance is to develop a deep understanding of the underlying commonalities among intertwined social/cognitive, information, and communications networks, and as a result improve our ability to analyze, predict, design, and influence complex systems interweaving many kinds of networks.

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2009年，美国陆军成立了网络科学 CTA，这是一个由陆军研究实验室、 CERDEC 和美国大约30个工业研发实验室和大学组成的联盟之间的合作研究联盟。这个联盟的目标是深入理解交织在一起的社会 / 认知、信息和通信网络之间的潜在共性，从而提高我们分析、预测、设计和影响交织在多种网络中的复杂系统的能力。

Subsequently, as a result of these efforts, the U.S. Department of Defense has sponsored numerous research projects that support Network Science.

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2009年，美国陆军成立了网络科学 CTA，这是一个由陆军研究实验室、 CERDEC 和美国大约30个工业研发实验室和大学组成的联盟之间的合作研究联盟。这个联盟的目标是深入理解交织在一起的社会 / 认知、信息和通信网络之间的潜在共性，从而提高我们分析、预测、设计和影响交织在多种网络中的复杂系统的能力。

随后，作为这些努力的结果，美国国防部赞助了许多支持网络科学的研究项目。

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