我有一组随机生成的正式图形，想计算每个图形的熵。换句话说，我有几个网络，想计算每个网络的信息量。
以下是两个包含图形熵正式定义的来源：
http://www.cs.washington.edu/homes/anuprao/pubs/CSE533Autumn2010/lecture4.pdf （PDF格式）
http://arxiv.org/abs/0711.4175v1
我需要的代码以图形作为输入（作为边列表或邻接矩阵），并输出比特数或其他某种信息内容度量。
由于我找不到任何实现此功能的代码，因此我打算根据正式定义从头开始编写代码。如果有人已经解决了这个问题并愿意分享代码，那将非常感激。
我最终使用了两种不同的论文来定义图熵：
复杂网络信息理论：演化与结构约束
R.V. Sole 和 S. Valverde（2004）
和
基于拓扑配置的网络熵及其在随机网络中的计算
B.H. Wang、W.X. Wang 和 T. Zhou
下面是计算每种方法的代码。代码假定您有一个无向无权图，没有自环。它以邻接矩阵作为输入，并返回以比特为单位的熵量。它是用R实现的，并利用了sna包。
graphEntropy <- function(adj, type="SoleValverde") {
if (type == "SoleValverde") {
return(graphEntropySoleValverde(adj))
}
else {
return(graphEntropyWang(adj))
}
}
graphEntropySoleValverde <- function(adj) {
# Calculate Sole & Valverde, 2004 graph entropy
# Uses Equations 1 and 4
# First we need the denominator of q(k)
# To get it we need the probability of each degree
# First get the number of nodes with each degree
existingDegrees = degree(adj)/2
maxDegree = nrow(adj) - 1
allDegrees = 0:maxDegree
degreeDist = matrix(0, 3, length(allDegrees)+1) # Need an extra zero prob degree for later calculations
degreeDist[1,] = 0:(maxDegree+1)
for(aDegree in allDegrees) {
degreeDist[2,aDegree+1] = sum(existingDegrees == aDegree)
}
# Calculate probability of each degree
for(aDegree in allDegrees) {
degreeDist[3,aDegree+1] = degreeDist[2,aDegree+1]/sum(degreeDist[2,])
}
# Sum of all degrees mult by their probability
sumkPk = 0
for(aDegree in allDegrees) {
sumkPk = sumkPk + degreeDist[2,aDegree+1] * degreeDist[3,aDegree+1]
}
# Equivalent is sum(degreeDist[2,] * degreeDist[3,])
# Now we have all the pieces we need to calculate graph entropy
graphEntropy = 0
for(aDegree in 1:maxDegree) {
q.of.k = ((aDegree + 1)*degreeDist[3,aDegree+2])/sumkPk
# 0 log2(0) is defined as zero
if (q.of.k != 0) {
graphEntropy = graphEntropy + -1 * q.of.k * log2(q.of.k)
}
}
return(graphEntropy)
}
graphEntropyWang <- function(adj) {
# Calculate Wang, 2008 graph entropy
# Uses Equation 14
# bigN is simply the number of nodes
# littleP is the link probability. That is the same as graph density calculated by sna with gden().
bigN = nrow(adj)
littleP = gden(adj)
graphEntropy = 0
if (littleP != 1 && littleP != 0) {
graphEntropy = -1 * .5 * bigN * (bigN - 1) * (littleP * log2(littleP) + (1-littleP) * log2(1-littleP))
}
return(graphEntropy)
}