of a node to a network is important

of a node to a network is important, we would prefer to have a centrality measure thatwould pick this up. For example, consider the network in Figure 2.2.4.In the network in Figure 2.2.4 the degree of nodes 3 and 5 are three, and the degreeof node 4 is only two. Arguably, node 4 is at least as central as nodes 3 and 5, andfar more central than the other nodes that each have two links (nodes 1, 2, 6, and7). There are several senses in which we see a powerful or central role of node 4.If one deletes node 4, the component structure of the network changes. This mightbe very important if we are thinking about something like information transmission,where node 4 is critical in path-connecting nodes 1 and 7. This will be picked up bya measure such as betweenness. We also see that node 4 is relatively close to all ofthe other nodes, in that it is at most two links away from any other node, whereaseach other node has at least one node at a distance of three or more. This would beimportant in applications where something is being conveyed or transmitted throughthe network (say an opinion or favor) and there is a decay of the strength with distance.In that case, being closer can either help a node make use of other nodes (e.g., havingaccess to favors) or to have ináuence (e.g., conveying opinions). This brings us to the64 CHAPTER 2. REPRESENTING AND MEASURING NETWORKSnext category of centrality measures.Closeness CentralityThis second class of measures keeps track of how close a given node is to each othernode. One obvious ìclosenessî-based measure is just the inverse of the average distancebetween i and any other node: (n 1)=Pj=i `(i; j), where `(i; j) is the number of linksin the shortest path between i and j. There are various conventions for handlingnetworks that are not connected, as well as other possible measures of distance, whichleads to a whole family of closeness measures.A richer way of measuring centrality based on closeness is to consider a decayparameter , where 1 > > 0 and then consider the proximity between a given nodeand each other node weighted by the decay. In particular, let the decay centrality of anode be deÖned asXj=i `(i;j);

of a node to a network is important, we would prefer to have a centrality measure thatwould pick this up. For example, consider the network in Figure 2.2.4.In the network in Figure 2.2.4 the degree of nodes 3 and 5 are three, and the degreeof node 4 is only two. Arguably, node 4 is at least as central as nodes 3 and 5, andfar more central than the other nodes that each have two links (nodes 1, 2, 6, and7). There are several senses in which we see a powerful or central role of node 4.If one deletes node 4, the component structure of the network changes. This mightbe very important if we are thinking about something like information transmission,where node 4 is critical in path-connecting nodes 1 and 7. This will be picked up bya measure such as betweenness. We also see that node 4 is relatively close to all ofthe other nodes, in that it is at most two links away from any other node, whereaseach other node has at least one node at a distance of three or more. This would beimportant in applications where something is being conveyed or transmitted throughthe network (say an opinion or favor) and there is a decay of the strength with distance.In that case, being closer can either help a node make use of other nodes (e.g., havingaccess to favors) or to have ináuence (e.g., conveying opinions). This brings us to the64 CHAPTER 2. REPRESENTING AND MEASURING NETWORKSnext category of centrality measures.Closeness CentralityThis second class of measures keeps track of how close a given node is to each othernode. One obvious ìclosenessî-based measure is just the inverse of the average distancebetween i and any other node: (n 1)=Pj=i `(i; j), where `(i; j) is the number of linksin the shortest path between i and j. There are various conventions for handlingnetworks that are not connected, as well as other possible measures of distance, whichleads to a whole family of closeness measures.A richer way of measuring centrality based on closeness is to consider a decayparameter , where 1 >  > 0 and then consider the proximity between a given nodeand each other node weighted by the decay. In particular, let the decay centrality of anode be deÖned asXj=i `(i;j);

0/5000

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目标语言: -

结果 (简体中文) 1: [复制]

复制成功！

将节点连接到网络很重要，我们希望有一个集中度指标来解决 这一问题。例如，考虑图2.2.4中的网络。 在图2.2.4的网络中，节点3和5的度数 为3，而节点4 的度数仅为2。可以说，节点4至少与节点3和5一样重要，并且 比每个都有两个链接的其他节点（节点1、2、6和 7）更重要。在多种意义上，我们可以看到节点4的强大或核心作用。 如果删除节点4，则网络的组件结构将发生变化。 如果我们正在考虑诸如信息传输之类的事情，这可能非常重要， 其中节点4在连接节点1和7的路径中至关重要。 诸如中间性之类的措施。我们还看到节点4相对靠近所有 其他节点，因为它距任何其他节点至多只有两个链接，而 每个其他节点至少有一个距离为三个或更多的节点。这 在通过 网络传输或传输某些东西（例如意见或主张）并且强度随距离而衰减的应用中将是重要的。 在那种情况下，靠近可以帮助一个节点利用其他节点（例如， 获得帮助）或产生影响（例如，传达意见）。这使我们进入第 64章第2章。表示和测量网络 下一类集中度测量。 亲密关系 第二类措施跟踪给定节点与其他 节点的距离。一个明显的基于ìclosenessî-措施仅仅是平均距离的逆 i和任何其他节点之间：（N 1）=点Pj = I`（I; j），其中`（I; j）为链路的数量 在i和j之间的最短路径。对于处理 未连接的网络，存在各种约定，以及其他可能的距离度量标准，这 导致了整个系列的接近性度量标准。 根据接近度测量中心度的一种更丰富的方法是考虑衰减 参数？，其中1>？> 0，然后考虑给定节点 与每个其他节点之间的接近度（由衰减加权）。特别地，让a的衰减中心 将节点定义为 Xj = i？（i; j）;

正在翻译中..

结果 (简体中文) 2:[复制]

复制成功！

of a node to a network is important, we would prefer to have a centrality measure that would pick this up. For example, consider the network in Figure 2.2.4. In the network in Figure 2.2.4 the degree of nodes 3 and 5 are three, and the degree of node 4 is only two. Arguably, node 4 is at least as central as nodes 3 and 5, and far more central than the other nodes that each have two links (nodes 1, 2, 6, and 7). There are several senses in which we see a powerful or central role of node 4. If one deletes node 4, the component structure of the network changes. This might be very important if we are thinking about something like information transmission, where node 4 is critical in path-connecting nodes 1 and 7. This will be picked up by a measure such as betweenness. We also see that node 4 is relatively close to all of the other nodes, in that it is at most two links away from any other node, whereas each other node has at least one node at a distance of three or more. This would be important in applications where something is being conveyed or transmitted through the network (say an opinion or favor) and there is a decay of the strength with distance. In that case, being closer can either help a node make use of other nodes (e.g., having access to favors) or to have ináuence (e.g., conveying opinions). This brings us to the 64 CHAPTER 2. REPRESENTING AND MEASURING NETWORKS next category of centrality measures. Closeness Centrality This second class of measures keeps track of how close a given node is to each other node. One obvious ìclosenessî-based measure is just the inverse of the average distance between i and any other node: (n 1)=Pj=i `(i; j), where `(i; j) is the number of links in the shortest path between i and j. There are various conventions for handling networks that are not connected, as well as other possible measures of distance, which leads to a whole family of closeness measures. A richer way of measuring centrality based on closeness is to consider a decay parameter , where 1 > > 0 and then consider the proximity between a given node and each other node weighted by the decay. In particular, let the decay centrality of a node be deÖned as Xj=i `(i;j);

正在翻译中..

结果 (简体中文) 3:[复制]

复制成功！

一个节点到一个网络的重要性，我们更希望有一个中心性度量 会捡起来的。例如，考虑图2.2.4中的网络。 在图2.2.4中的网络中，节点3和节点5的阶数为3，并且 节点4的只有两个。可以说，节点4至少和节点3和节点5一样中心，并且 比每个节点都有两个链接（节点1、2、6和 7）一。我们在四个节点中看到了一个重要的角色。 如果删除节点4，则网络的组件结构将发生变化。这可能 如果我们考虑的是像信息传输这样的东西， 其中节点4在连接节点1和7的路径中是关键的。这将由 中间性一种度量，如中间性。我们还可以看到节点4与 其他节点，因为它与任何其他节点之间最多有两个链接，而 每个其他节点在三个或更多的距离处至少有一个节点。这应该是 重要的是在应用中某物被传送或传送 网络（比如一个观点或是一个好意）的力量会随着距离而衰减。 在这种情况下，更近一点可以帮助一个节点利用其他节点（例如 获得帮助）或有影响力（例如，传达意见）。这就把我们带到了 64第2章。表示和测量网络 下一类集中度指标。 封闭中心性 第二类度量跟踪给定节点之间的距离 节点。一个明显的基于“贴近度”的测量方法是平均距离的倒数 在i和任何其他节点之间：（n1）=Pj=i`（i；j），其中`（i；j）是链路数 在i和j之间的最短路径中，有各种各样的处理约定 未连接的网络，以及其他可能的距离度量 导致了一系列的亲密措施。 基于接近度测量中心度的一种更丰富的方法是考虑衰变 参数，其中1>>0，然后考虑给定节点之间的接近度 每个节点都被衰变加权。特别是，让 节点定义为 Xj=i `（i；j）；

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