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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.

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，这是一个定义松散的网络拓扑网络，它包含有许多连接的枢纽顶点，这些连接以一种保持连接数量与所有其他节点数量之间恒定比率的方式增长。尽管许多网络，比如互联网，似乎保持了这一点，但是其他网络的节点分布长尾分布仅仅接近无标度比例。

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。

 

 

 

===Department of Defense initiatives===

===Department of Defense initiatives===

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.

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.

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:

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: