18
个编辑
更改
跳到导航
跳到搜索
第279行：
第279行： − 为了保持BA模型中的优先链接，该适应度乘以基于度分布的优先链接，得到连接到节点 i 的真实概率。+ 第295行：
第295行： − + 第321行：
第321行： − 由于节点可能会以一定的概率从网络中移除，因此会出现更多的复杂情况。此外，节点之间现有的链接可能会被删除并且创建新的链接。这些行为发生的概率可能取决于时间，也可能与节点的适应度有关。通过研究有关网络的特性，可以为这些事件赋予概率，从而生成具有相同特性的模型网络。这种增长将在每个时间步骤中发生下列行为之一:+ 第361行：
第361行： − 除了上面描述的不断增长的网络模型之外，可能有时候其他方法对于描述演化网络的某些性质更有用或更方便。+ − − − 在竞争性决策发生的网络系统中，博弈论经常被用来建立系统动力学模型，趋向均衡可以被认为是拓扑进化的驱动力。例如 Kasthurirathna 和 Piraveenan 表明，当一个系统中的个体表现出不同程度的理性时，提高整个系统的理性可能是无标度网络出现的进化原因。他们通过对一个最初的随机网络施加进化压力来模拟一系列经典博弈，当允许重新连接时，网络收敛到纳什均衡，从而证明了这一点。在这个过程中，网络变得越来越无标度。 第374行：
第371行： + 第404行：
第402行： + + 第411行：
第411行： − 观察不断演化的网络最常用的方法是把它们看作连续的静态网络。这可以概念化为组成电影的一个个静态图像。有许多简单的参数可以描述一个静态网络（节点数、边、路径长度、连通子图），或者描述图中的特定节点，比如链接数或集聚系数。然后可以使用信号处理概念将这些属性分别作为时间序列进行研究。例如，我们可以通过查看网络的连续快照并计算每个快照中的链接数量，来跟踪每分钟建立到服务器的链接数量。+ 第442行：
第442行： − + − 第449行：
第448行： − + − − 那些将演化网络视为一系列快照不能直接观察到的特性可能很重要，例如节点之间的接触时间。可以定义其他类似的属性，然后可以通过网络的演化来跟踪这些属性，并直接可视化它们。 第459行：
第456行： − + 第531行：
第528行： − + + − Another issue with using successive snapshots is that only slight changes in network topology can have large effects on the outcome of algorithms designed to find communities. Therefore, it is necessary to use a non classical definition of communities which permits following the evolution of the community through a set of rules such as birth, death, merge, split, growth, and contraction.<ref name="Quantifying social group evolution">{{Cite journal+ 第689行：
第687行： − − 使用连续快照的另一个问题是，在网络拓扑中微小的变化可以对用于寻找网络社区的算法的结果产生巨大的影响。因此，有必要使用一个非经典的社区定义，它允许通过一系列的规则，如出生、死亡、合并、分裂、生长和收缩，跟随社区的演变。 第698行：
第694行： − 2009年世界预定商业航空交通路线图。这个网络随着新路线的调度或取消而不断发展。+ 第704行：
第700行： − 几乎所有真实世界的网络都是不断演化的网络，因为它们是随着时间的推移而构建的。通过改变上述各自的概率，可以使用扩展的 BA 模型来构造一个具有与许多观测网络几乎相同属性的网络。 生活中的网络: 比例特性和特征值谱{ Cite journal+
无编辑摘要
In order to preserve the preferential attachment from the BA model, this fitness is then multiplied by the preferential attachment based on degree distribution to give the true probability that a link is created which connects to node i.
In order to preserve the preferential attachment from the BA model, this fitness is then multiplied by the preferential attachment based on degree distribution to give the true probability that a link is created which connects to node i.
为了保持BA模型中的偏好依附，该适应度乘以基于度分布的偏好依附，得到连接到节点i的真实概率。
Where <math>\eta</math> is the fitness, which may also depend on time. A decay of fitness with respect to time may occur and can be formalized by
Where <math>\eta</math> is the fitness, which may also depend on time. A decay of fitness with respect to time may occur and can be formalized by
其中<math>\eta</math>是适应度，这也可能依赖时间。适应度可能随时间衰减，可以表示为
其中<math>\eta</math>是适应度，这也可能依赖于时间。适应度可能随时间衰减，可以表示为
Further complications arise because nodes may be removed from the network with some probability. Additionally, existing links may be destroyed and new links between existing nodes may be created. The probability of these actions occurring may depend on time and may also be related to the node's fitness. Probabilities can be assigned to these events by studying the characteristics of the network in question in order to grow a model network with identical properties. This growth would take place with one of the following actions occurring at each time step:
Further complications arise because nodes may be removed from the network with some probability. Additionally, existing links may be destroyed and new links between existing nodes may be created. The probability of these actions occurring may depend on time and may also be related to the node's fitness. Probabilities can be assigned to these events by studying the characteristics of the network in question in order to grow a model network with identical properties. This growth would take place with one of the following actions occurring at each time step:
由于节点可能会以一定的概率从网络中移除，因此会出现更多的复杂情况。此外，节点之间现有的链接可能会被删除并且创建新的链接。这些行为发生的概率可能依赖于时间，也可能与节点的适应度有关。通过研究有关网络的特性，可以为这些事件赋予概率，从而生成具有相同特性的模型网络。这种增长将在每个时间步骤中发生下列行为之一:
In addition to growing network models as described above, there may be times when other methods are more useful or convenient for characterizing certain properties of evolving networks.
In addition to growing network models as described above, there may be times when other methods are more useful or convenient for characterizing certain properties of evolving networks.
除了上面描述的不断生长的网络模型之外，可能有时候其他方法对于描述演化网络的某些性质更有用或更方便。
===Convergence towards equilibria 趋向均衡===
===Convergence towards equilibria 趋向均衡===
In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan <ref>{{cite journal
In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan <ref>{{cite journal
In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan <ref>{{cite journal
In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan <ref>{{cite journal
在竞争性决策发生的网络系统中，博弈论经常被用来建模系统动力学，趋向均衡可以被认为是拓扑进化的驱动力。例如Kasthurirathna和Piraveenan表明，
参考{ cite journal
参考{ cite journal
|volume=In Press |date=2015}}</ref> have shown that when individuals in a system display varying levels of rationality, improving the overall system rationality might be an evolutionary reason for the emergence of scale-free networks. They demonstrated this by applying evolutionary pressure on an initially random network which simulates a range of classic games, so that the network converges towards Nash equilibria while being allowed to re-wire. The networks become increasingly scale-free during this process.
|volume=In Press |date=2015}}</ref> have shown that when individuals in a system display varying levels of rationality, improving the overall system rationality might be an evolutionary reason for the emergence of scale-free networks. They demonstrated this by applying evolutionary pressure on an initially random network which simulates a range of classic games, so that the network converges towards Nash equilibria while being allowed to re-wire. The networks become increasingly scale-free during this process.
当一个系统中的个体表现出不同程度的理性时，提高整个系统的理性可能是无标度网络出现的进化原因。他们通过对一个最初的随机网络施加进化压力来模拟一系列经典博弈，当允许重新连接时，网络收敛到纳什均衡，从而证明了这一点。在这个过程中，网络变得越来越无标度。
===Treat evolving networks as successive snapshots of a static network 视演化网络为连续的静态网络快照===
===Treat evolving networks as successive snapshots of a static network 视演化网络为连续的静态网络快照===
The most common way to view evolving networks is by considering them as successive static networks. This could be conceptualized as the individual still images which compose a motion picture. Many simple parameters exist to describe a static network (number of nodes, edges, path length, connected components), or to describe specific nodes in the graph such as the number of links or the clustering coefficient. These properties can then individually be studied as a time series using signal processing notions.<ref name=EvolvingNetworksPDF>{{Cite journal
The most common way to view evolving networks is by considering them as successive static networks. This could be conceptualized as the individual still images which compose a motion picture. Many simple parameters exist to describe a static network (number of nodes, edges, path length, connected components), or to describe specific nodes in the graph such as the number of links or the clustering coefficient. These properties can then individually be studied as a time series using signal processing notions.<ref name=EvolvingNetworksPDF>{{Cite journal
观察不断演化的网络最常用的方法是把它们看作连续的静态网络。这可以概念化为组成电影的一个个静态图像。有许多简单的参数可以描述一个静态网络（节点数、边、路径长度、连通子图），或者描述图中的特定节点，比如链接数或集聚系数。然后可以使用信号处理概念将这些属性单独作为时间序列进行研究。
|display-authors=etal}}</ref> For example, we can track the number of links established to a server per minute by looking at the successive snapshots of the network and counting these links in each snapshot.
|display-authors=etal}}</ref> For example, we can track the number of links established to a server per minute by looking at the successive snapshots of the network and counting these links in each snapshot.
例如，我们可以通过查看网络的连续快照并计算每个快照中的链接数量，来跟踪每分钟建立到服务器的链接数量。
Unfortunately, the analogy of snapshots to a motion picture also reveals the main difficulty with this approach: the time steps employed are very rarely suggested by the network and are instead arbitrary. Using extremely small time steps between each snapshot preserves resolution, but may actually obscure wider trends which only become visible over longer timescales. Conversely, using larger timescales loses the temporal order of events within each snapshot. Therefore, it may be difficult to find the appropriate timescale for dividing the evolution of a network into static snapshots.
Unfortunately, the analogy of snapshots to a motion picture also reveals the main difficulty with this approach: the time steps employed are very rarely suggested by the network and are instead arbitrary. Using extremely small time steps between each snapshot preserves resolution, but may actually obscure wider trends which only become visible over longer timescales. Conversely, using larger timescales loses the temporal order of events within each snapshot. Therefore, it may be difficult to find the appropriate timescale for dividing the evolution of a network into static snapshots.
Unfortunately, the analogy of snapshots to a motion picture also reveals the main difficulty with this approach: the time steps employed are very rarely suggested by the network and are instead arbitrary. Using extremely small time steps between each snapshot preserves resolution, but may actually obscure wider trends which only become visible over longer timescales. Conversely, using larger timescales loses the temporal order of events within each snapshot. Therefore, it may be difficult to find the appropriate timescale for dividing the evolution of a network into static snapshots.
Unfortunately, the analogy of snapshots to a motion picture also reveals the main difficulty with this approach: the time steps employed are very rarely suggested by the network and are instead arbitrary. Using extremely small time steps between each snapshot preserves resolution, but may actually obscure wider trends which only become visible over longer timescales. Conversely, using larger timescales loses the temporal order of events within each snapshot. Therefore, it may be difficult to find the appropriate timescale for dividing the evolution of a network into static snapshots.
不幸的是，快照与电影的类比也揭示了这种方法的主要困难: 使用的时间步骤很少由网络给出，而是任意的。在每个快照之间使用极小的时间步骤可以保持分辨率，但实际上可能掩盖了只有在较长时间尺度下才能看到的更广泛的趋势。相反，使用较大的时间尺度会失去每个快照中事件的时间顺序。因此，可能很难找到合适的时间尺度来将网络的演变划分为静态快照。
不幸的是，快照与电影的类比也揭示了这种方法的主要困难: 使用的时间步骤很少由网络给出，而是任意的。在每个快照之间使用极小的时间步骤可以保持分辨率，但实际上可能掩盖了只有在较长时间尺度下才能看到的更广泛的趋势。相反，使用较大的时间尺度会失去每个快照中事件的时间顺序。因此，可能很难找到合适的时间尺度来将网络的演化划分为静态快照。
===Define dynamic properties 定义动力学性质===
===Define dynamic properties 定义动力学性质===
It may be important to look at properties which cannot be directly observed by treating evolving networks as a sequence of snapshots, such as the duration of contacts between nodes<ref name="Impact of human mobility on the
It may be important to look at properties which cannot be directly observed by treating evolving networks as a sequence of snapshots, such as the duration of contacts between nodes<ref name="Impact of human mobility on the
It may be important to look at properties which cannot be directly observed by treating evolving networks as a sequence of snapshots, such as the duration of contacts between nodes<ref name="Impact of human mobility on the
It may be important to look at properties which cannot be directly observed by treating evolving networks as a sequence of snapshots, such as the duration of contacts between nodes<ref name="Impact of human mobility on the
那些不能直接从将演化网络视为一系列快照中观察到的特性可能很重要，例如节点之间的接触时间。
design of opportunistic forwarding algorithms">{{Cite journal
design of opportunistic forwarding algorithms">{{Cite journal
}}</ref> Other similar properties can be defined and then it is possible to instead track these properties through the evolution of a network and visualize them directly.
}}</ref> Other similar properties can be defined and then it is possible to instead track these properties through the evolution of a network and visualize them directly.
} / ref
} / ref 可以定义其他类似的属性，然后可以通过网络的演化来跟踪这些属性，并直接可视化它们。
Another issue with using successive snapshots is that only slight changes in network topology can have large effects on the outcome of algorithms designed to find communities. Therefore, it is necessary to use a non classical definition of communities which permits following the evolution of the community through a set of rules such as birth, death, merge, split, growth, and contraction.<ref name="Quantifying social group evolution">{{Cite journal
Another issue with using successive snapshots is that only slight changes in network topology can have large effects on the outcome of algorithms designed to find communities. Therefore, it is necessary to use a non classical definition of communities which permits following the evolution of the community through a set of rules such as birth, death, merge, split, growth, and contraction.<ref name="Quantifying social group evolution">{{Cite journal
Another issue with using successive snapshots is that only slight changes in network topology can have large effects on the outcome of algorithms designed to find communities. Therefore, it is necessary to use a non classical definition of communities which permits following the evolution of the community through a set of rules such as birth, death, merge, split, growth, and contraction.<ref name="Quantifying social group evolution">{{Cite journal
使用连续快照的另一个问题是，在网络拓扑中微小的变化可以对用于寻找网络社团的算法的结果产生巨大的影响。因此，有必要使用一个非经典的社团定义，它允许通过一系列的规则，如出生、死亡、合并、分裂、生长和收缩，来跟随社团的演化。
量化社会群体进化{ Cite journal
量化社会群体进化{ Cite journal
{} / ref
{} / ref
==Applications 应用==
==Applications 应用==
Route map of the world's scheduled commercial airline traffic, 2009. This network evolves continuously as new routes are scheduled or cancelled.
Route map of the world's scheduled commercial airline traffic, 2009. This network evolves continuously as new routes are scheduled or cancelled.
2009年世界预定商业航空交通路线图。这个网络随着新路线的计划或取消而不断演变。
Almost all real world networks are evolving networks since they are constructed over time. By varying the respective probabilities described above, it is possible to use the expanded BA model to construct a network with nearly identical properties as many observed networks.<ref name="Networks in life: scaling properties and eigenvalue spectra">{{Cite journal
Almost all real world networks are evolving networks since they are constructed over time. By varying the respective probabilities described above, it is possible to use the expanded BA model to construct a network with nearly identical properties as many observed networks.<ref name="Networks in life: scaling properties and eigenvalue spectra">{{Cite journal
Almost all real world networks are evolving networks since they are constructed over time. By varying the respective probabilities described above, it is possible to use the expanded BA model to construct a network with nearly identical properties as many observed networks.<ref name="Networks in life: scaling properties and eigenvalue spectra">{{Cite journal
Almost all real world networks are evolving networks since they are constructed over time. By varying the respective probabilities described above, it is possible to use the expanded BA model to construct a network with nearly identical properties as many observed networks.<ref name="Networks in life: scaling properties and eigenvalue spectra">{{Cite journal
几乎所有真实世界的网络都是不断演化的网络，因为它们是随着时间的推移而构建的。通过改变上述各自的概率，可以使用扩展的BA模型来构造一个具有与许多观测网络几乎相同属性的网络。 生活中的网络: 比例特性和特征值谱{ Cite journal
|url = http://www.barabasilab.com/pubs/CCNR-ALB_Publications/200211-01_PhysA-NetworksInLife/200211-01_PhysA-NetworksInLife.pdf
|url = http://www.barabasilab.com/pubs/CCNR-ALB_Publications/200211-01_PhysA-NetworksInLife/200211-01_PhysA-NetworksInLife.pdf