efficiency(sna)
efficiency()所属R语言包：sna
Compute Graph Efficiency Scores
计算图效率值
译者：生物统计家园网 机器人LoveR
描述----------Description----------
efficiency takes one or more graphs (dat) and returns the Krackhardt efficiency scores for the graphs selected by g.
efficiency需要一个或多个图形（dat）和返回的Krackhardt的效率得分的图形选择g。
用法----------Usage----------
efficiency(dat, g=NULL, diag=FALSE)
参数----------Arguments----------
参数：dat
one or more graphs.
一个或多个图形。
参数：g
index values for the graphs to be utilized; by default, all graphs are selected.
可以利用的索引值的图形，默认情况下，所有的图形被选中。
参数：diag
TRUE if the diagonal contains valid data; by default, diag==FALSE.
TRUE如果对角线包含有效的数据，默认情况下，diag==FALSE。
Details
详细信息----------Details----------
Let G= G_1 U ... U G_n be a digraph with weak components G_1,G_2,...,G_n. For convenience, we denote the cardinalities of these components' vertex sets by |V(G)|=N and |V(G_i)|=N_i, for i in 1,...,n. Then the Krackhardt efficiency of G is given by
让我们G= G_1 U ... U G_n是一个有向图与弱组件G_1,G_2,...,G_n。为方便起见，我们用这些组件的顶点集的基数|V(G)|=N和|V(G_i)|=N_i，for i in 1,...,n。然后在Krackhardt的效率G给出了
1 - ( |E(G)| - Sum(N_i-1,i=1,..,n) )/( Sum(N_i(N_i-1) - (N_i-1),i=1,..,n) )</i>
1 - （| E（G）| - 萨姆（N_i-1，= 1，...，N））/（SUM（N_i（N_i-1） - （N_i-1），i = 1，...， N））</ P>
which can be interpreted as 1 minus the proportion of possible “extra” edges (above those needed to weakly connect the existing components) actually present in the graph. A graph which an efficiency of 1 has precisely as many edges as are needed to connect its components; as additional edges are added, efficiency gradually falls towards 0.
这可以解释为1的比例减去可能的“额外”的边缘（上述那些所需的弱连接的现有组件）图中的实际存在。一个图表，效率为1的正是许多边缘所需要的连接组件添加额外的边缘，效率逐渐降低趋近于0。
Efficiency is one of four measures (connectedness, efficiency, hierarchy, and lubness) suggested by Krackhardt for summarizing hierarchical structures. Each corresponds to one of four axioms which are necessary and sufficient for the structure in question to be an outtree; thus, the measures will be equal to 1 for a given graph iff that graph is an outtree. Deviations from unity can be interpreted in terms of failure to satisfy one or more of the outtree conditions, information which may be useful in classifying its structural properties.
效率的四项措施（connectedness，efficiency，hierarchy和lubness）所建议的Krackhardt总结分层结构。每个对应于一个四个公理，它是必要的和足够的结构中的问题是一个outtree;因此，措施将等于1，对于一个给定的曲线图，当且仅当该图形是一个outtree。团结偏离可以被解释方面的失败，以满足一个或多个的outtree的条件下，这可能是有用的信息，在其结构性能分类。
值----------Value----------
A vector of efficiency scores
一个向量的效率值
注意----------Note----------
The four Krackhardt indices are, in general, nondegenerate for a relatively narrow band of size/density combinations (efficiency being the sole exception). This is primarily due to their dependence on the reachability graph, which tends to become complete rapidly as size/density increase. See Krackhardt (1994) for a useful simulation study.
四个Krackhardt指数是，在一般情况下，非简并为相对窄的频带的大小/密度组合（效率是唯一的例外）。这主要是因为他们依赖的可达图，这往往成为完整的大小/密度迅速增加。见Krackhardt（1994年）进行了有益的模拟研究。
（作者）----------Author(s)----------
Carter T. Butts <a href="mailto:buttsc@uci.edu">buttsc@uci.edu</a>
参考文献----------References----------
<h3>See Also</h3>
实例----------Examples----------
#Get efficiency scores for graphs of varying densities[效率值不同密度的图形]
efficiency(rgraph(10,5,tprob=c(0.1,0.25,0.5,0.75,0.9)))
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
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发表于 2012-9-30 10:50:35
