bonpow(sna)
bonpow()所属R语言包：sna
Find Bonacich Power Centrality Scores of Network Positions
Bonacich电源，掌得分的网络位置
译者：生物统计家园网 机器人LoveR
描述----------Description----------
bonpow takes one or more graphs (dat) and returns the Boncich power centralities of positions (selected by nodes) within the graphs indicated by g. The decay rate for power contributions is specified by exponent (1 by default). This function is compatible with centralization, and will return the theoretical maximum absolute deviation (from maximum) conditional on size (which is used by centralization to normalize the observed centralization score).
bonpowdat需要一个或多个图形（nodes）和返回的Boncich电源的位置（选择g）在图形的中心性。 exponent（缺省值为1）指定的电源贡献的衰减率。此功能适用于与centralization，将返回理论上的最大绝对偏差（最大），有条件的大小（它是由centralization标准化集中观察到的得分）。
用法----------Usage----------
bonpow(dat, g=1, nodes=NULL, gmode="digraph", diag=FALSE,
tmaxdev=FALSE, exponent=1, rescale=FALSE, tol=1e-07)
参数----------Arguments----------
参数：dat
one or more input graphs.
一个或多个输入图表。
参数：g
integer indicating the index of the graph for which centralities are to be calculated (or a vector thereof). By default, g=1.
整数，指示其中中心性计为（或它们的向量）的曲线图的索引。默认情况下，g= 1。
参数：nodes
vector indicating which nodes are to be included in the calculation. By default, all nodes are included.
矢量的指示哪些节点要被包括在计算中。默认情况下，所有的节点都包括在内。
参数：gmode
string indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. This is currently ignored.
的图表类型的字符串，表示正在评估中。 "digraph"表示的边缘应被解释为指示;"graph"表明边缘是无向的。这是目前被忽略的。
参数：diag
boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. Diag is FALSE by default.
布尔值，表示是否对角线应被视为有效的数据。设置这是真的，当且仅当数据可以包含循环。 Diag是FALSE默认情况下。
参数：tmaxdev
boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, tmaxdev=FALSE.
布尔值，表示是否从最大的节点的中心性的理论最大绝对偏差应返回。默认情况下，tmaxdev=FALSE。
参数：exponent
exponent (decay rate) for the Bonacich power centrality score; can be negative
可以是负数指数（衰减率）为Bonacich权力核心得分;
参数：rescale
if true, centrality scores are rescaled such that they sum to 1.
如果为true，中心的分数重新调整，他们总结到1。
参数：tol
tolerance for near-singularities during matrix inversion (see solve)
容忍接近奇点矩阵求逆（见solve）
Details
详细信息----------Details----------
Bonacich's power centrality measure is defined by C_BP(alpha,beta)=alpha (I-A)^-1 A 1, where beta is an attenuation parameter (set here by exponent) and A is the graph adjacency matrix. (The coefficient alpha acts as a scaling parameter, and is set here (following Bonacich (1987)) such that the sum of squared scores is equal to the number of vertices. This allows 1 to be used as a reference value for the “middle” of the centrality range.) When beta->1/lambda_A1 (the reciprocal of the largest eigenvalue of A), this is to within a constant multiple of the familiar eigenvector centrality score; for other values of β, the behavior of the measure is quite different. In particular, β gives positive and negative weight to even and odd walks, respectively, as can be seen from the series expansion C_BP(alpha,beta) = alpha sum( beta^k A^(k+1) 1, k in 0..infinity ) which converges so long as |beta|<1/lambda_A1. The magnitude of beta controls the influence of distant actors on ego's centrality score, with larger magnitudes indicating slower rates of decay. (High rates, hence, imply a greater sensitivity to edge effects.)
Bonacich的权力核心措施是指由C_BP(alpha,beta)=alpha (I-A)^-1 A 1，beta是衰减参数（在此设置的exponent）A是图的邻接矩阵。 （系数alpha作为缩放参数的行为，并且在这里被设置（以下Bonacich（1987年））的平方分数的总和，使得等于顶点的数目。这允许1被用来作为一个参考值为“中间”的核心范围内。）当beta->1/lambda_A1（的最大特征值的倒数A），这是在熟悉的特征向量中心得分乘以某个常数;为其他值的行为的措施的β，是完全不同的。特别是，β给出了阳性和阴性的重量为偶数和奇数的散步，分别可以看出，从级数展开C_BP(alpha,beta) = alpha sum( beta^k A^(k+1) 1, k in 0..infinity )收敛，只要|beta|<1/lambda_A1。 beta的大小控制遥远的演员自我的核心比分，表明较慢的衰变率有较大程度的影响。 （高利率，因此，这意味着一个更敏感的边缘效应。）
Interpretively, the Bonacich power measure corresponds to the notion that the power of a vertex is recursively defined by the sum of the power of its alters. The nature of the recursion involved is then controlled by the power exponent: positive values imply that vertices become more powerful as their alters become more powerful (as occurs in cooperative relations), while negative values imply that vertices become more powerful only as their alters become weaker (as occurs in competitive or antagonistic relations). The magnitude of the exponent indicates the tendency of the effect to decay across long walks; higher magnitudes imply slower decay. One interesting feature of this measure is its relative instability to changes in exponent magnitude (particularly in the negative case). If your theory motivates use of this measure, you should be very careful to choose a decay parameter on a non-ad hoc basis.
阐释，Bonacich的功率测量相对应的概念，即一个顶点的力量的总和，其改变的力量是递归的定义。所涉及的递归性质，然后控制的幂指数：正面的价值观意味着顶点变得更加强大，因为他们的改变变得更加强大（合作关系），而负值意味着顶点变得更加强大，只因为他们的改变成为较弱（如发生在竞争或对立关系）。指数值表明跨越长距离散步的效果衰减的趋势，更高的幅度意味着较慢的衰变。这一措施的一个有趣的特性是其相对不稳定性指数大小的变化（特别是在负的情况下）。如果你的理论，这项措施的动机，你应该非常小心地选择一个非临时性的衰减参数。
值----------Value----------
A vector, matrix, or list containing the centrality scores (depending on the number and size of the input graphs).
含有的中心得分（取决于上的输入图形的数量和大小）的向量，矩阵，或列表。
警告----------Warning ----------
Singular adjacency matrices cause no end of headaches for this algorithm; thus, the routine may fail in certain cases. This will be fixed when I get a better algorithm. bonpow will not symmetrize your data before extracting eigenvectors; don't send this routine asymmetric matrices unless you really mean to do so.
奇异的邻接矩阵导致头痛这个算法没有尽头的，因此，该程序可以在某些情况下失败。这将是固定的，当我得到一个更好的算法。 bonpow不会对称数据，然后提取特征向量;不发送这种常规的非对称矩阵，除非你真的是这样做的。
注意----------Note----------
The theoretical maximum deviation used here is not obtained with the star network, in general. For positive exponents, at least, the symmetric maximum occurs for an empty graph with one complete dyad (the asymmetric maximum is generated by the outstar). UCINET V seems not to adjust for this fact, which can cause some oddities in their centralization scores (thus, don't expect to get the same numbers with both packages).
这里所用的理论最大偏差不能得到的星形网络，一般。对于正指数，至少出现对称的最大值的一个空的图形与一个完整的对子（不对称最大由outstar产生的）。 UCINET V似乎并没有调整这一事实，可能会导致一些古怪的集中的分数（因此，不要指望得到相同的号码，这两个软件包）。
（作者）----------Author(s)----------
Carter T. Butts <a href="mailto:buttsc@uci.edu">buttsc@uci.edu</a>
参考文献----------References----------
Bonacich, P. (1987). &ldquo ower and Centrality: A Family of Measures.” American Journal of Sociology, 92, 1170-1182.
参见----------See Also----------
centralization, evcent
centralization，evcent
实例----------Examples----------
#Generate some test data[生成一些测试数据。]
dat<-rgraph(10,mode="graph")
#Compute Bonpow scores[计算Bonpow分数]
bonpow(dat,exponent=1,tol=1e-20)
bonpow(dat,exponent=-1,tol=1e-20)
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。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
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发表于 2012-9-30 10:48:39
