lubness(sna)
lubness()所属R语言包：sna
Compute Graph LUBness Scores
计算图表LUBness成绩
译者：生物统计家园网 机器人LoveR
描述----------Description----------
lubness takes a graph set (dat) and returns the Krackhardt LUBness scores for the graphs selected by g.
lubness的曲线图集（dat）和返回Krackhardt LUBness分数由g选择的曲线图。
用法----------Usage----------
lubness(dat, g=NULL)
参数----------Arguments----------
参数：dat
one or more input graphs.
一个或多个输入图表。
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。
Details
详细信息----------Details----------
In the context of a directed graph G, two actors i and j may be said to have an upper bound iff there exists some actor k such that directed ki and kj paths belong to G. An upper bound l is known as a least upper bound for i and j iff it belongs to at least one ki and kj path (respectively) for all i,j upper bounds k; let L(i,j) be an indicator which returns 1 iff such an l exists, otherwise returning 0. Now, let G_1,G_2,...,G_n represent the weak components of G. For convenience, we denote the cardinalities of these graphs' vertex sets by |V(G)|=N and |V(G_i)|=N_i, for i in 1,...,n. Given this, the Krackhardt LUBness of G is given by
在一个有向图G，两位演员i和j可以说是有一个上限的，当且仅当存在一些演员k等定向<X的背景下， >和ki路径属于kj。一个上界G被称为最小上限为l和i当且仅当它是属于至少一个j和ki路径（）所有的kj上限i,j;让k是一个指标，则返回1，当且仅当这样的L(i,j)存在，否则返回0。现在，让我们l代表的G_1,G_2,...,G_n弱。为方便起见，我们用这些图的顶点集的基数G和|V(G)|=N，|V(G_i)|=N_i。鉴于此，Krackhardt LUBnessfor i in 1,...,n给出了
1-Sum(Sum(1-L(v_j,v_k),v_j,v_k in V(G_i)),i=1,...,n)/Sum((N_i-1)(N_i-2)/2,i=1,...,n)</i>
1-SUM（求和（1 L（v_j，v_k），v_j，v_k V（G_i）），i = 1，...，N）/ SUM（（N_i-1）（N_i-2）/ 2 ，i = 1，...，N）</ I>
Where all vertex pairs possess a least upper bound, Krackhardt's LUBness is equal to 1; in general, it approaches 0 as this condition is broached. (This convergence is problematic in certain cases due to the requirement that we sum violations across components; where a graph contains no components of size three or greater, Krackhardt's LUBness is not well-defined. lubness returns a NaN in these cases.)
对所有顶点具有最小上界，Krackhardt的LUBness等于1，在一般情况下，接近0，这种情况下开始讨论。 （这种融合是有问题的，在某些情况下，由于要求，我们的违规行为在各个组件中，其中图3或更高，Krackhardt的LUBness没有得到很好的定义不包含任何部件的尺寸。lubness返回一个NaN在这种情况下。）
LUBness 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.
LUBness是其中的四项措施（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 LUBness scores
LUBness分数的矢量
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 LUBness scores for graphs of varying densities[获取LUBness成绩，为不同密度的图形]
lubness(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：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
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发表于 2012-9-30 10:56:14
