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Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes (or vertices) and the connections between the elements or actors as links (or edges). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."[1]

Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes (or vertices) and the connections between the elements or actors as links (or edges). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."[1]

网络科学是一个研究复杂网络的学术领域，如通讯网络，计算机网络，生物网络，认知和语义网络，以及社会网络，考虑不同的元素或参与者表示的节点(或顶点)和元素或参与者之间的联系作为链接(或边)。 这个领域的理论和方法包括数学的图理论，物理学的统计力学，计算机科学的数据挖掘和信息可视化，统计学的推理建模，社会学的社会结构。 美国国家研究委员会将巴拉巴西网络科学定义为“研究物理、生物和社会现象的网络表征，从而得出这些现象的预测模型。” [1]

网络科学Network Science是一个研究复杂网络的学术领域，如通讯网络，计算机网络，生物网络，认知和语义网络，以及社会网络，主要由节点（顶点）表示不同元素或参与者，由连边表示元素和参与者之间的联系。这个领域的理论和方法包括数学的图理论，物理学的统计力学，计算机科学的数据挖掘和信息可视化，统计学的推理建模，社会学的社会结构。 美国国家研究委员会The United States National Research Council将网络科学定义为“研究物理、生物和社会现象的网络表征，从而得出这些现象的预测模型。” [1]

== Background and history ==

== Background and history ==

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).

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).

[[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>

[[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>

[[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]].

[[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]].

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.

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.