iGraph -k-核与graph.coreness低估了一些核

Question

我用R中的iGraph来计算10个节点的k核.这些节点中有8个是连通的，其度为5或更大，而另外两个节点的度仅为3。

根据我对k核的理解，所有连接并且至少有5度的8个节点不是都在一个值为5的k核中吗？然而，这8家公司中有两家的k核心价值分别为4和3.

见下面可复制的图表：

el = matrix(c("Ns-1","Ns-1","Ns-1","Ns-1","Ns-1","Ns-1","Ns-1","Ns-1","Ns-14","Ns-14","Ns-15","Ns-15","Ns-15","Ns-17","Ns-17","Ns-17","Ns-17","Ns-2","Ns-2","Ns-2","Ns-2","Ns-4","Ns-4","Ns-4","Ns-5","Ns-5","Ns-5","TAMU-7","Ns-14","Ns-15","Ns-17","Ns-2","Ns-4","Ns-5","TAMU-7","TAMU-8","Ns-15","Ns-17","Ns-17","Ns-4","Ns-18","Ns-2","Ns-4","Ns-5","Ns-18","Ns-4","Ns-5","TAMU-7","TAMU-8","Ns-5","TAMU-7","TAMU-8","TAMU-7","TAMU-8","Ns-18","TAMU-8"),nrow=28,ncol=2)

graph = graph.edgelist(el[,1:2],directed=F)

l <- layout.kamada.kawai(graph)
V(graph)$x <- l[,1]
V(graph)$y <- l[,2]

V(graph)$kCore = graph.coreness(graph)
V(graph)$degree = degree(graph)

layout(matrix(c(1,2), 1, 2))
plot(graph,
 main="Degree",
 vertex.size = 20,
 vertex.label = V(graph)$degree,
 vertex.label.color = "black",
 vertex.label.font = 1,
 vertex.label.family = "sans",
 vertex.label.cex = 1,
 vertex.color = "white")

plot(graph,
 main="K Cores",
 vertex.size = 20,
 vertex.label = V(graph)$kCore,
 vertex.label.color = "black",
 vertex.label.font = 1,
 vertex.label.family = "sans",
 vertex.label.cex = 1,
 vertex.color = "white")

..。它产生了这个图(https://www.dropbox.com/s/unkkgodf8ppteyq/igraph.png?dl=0)，它的程度在左边，k核显示在右边。

基本上，左上角和右上角的节点都应该有3的度和k核，其余的应该是5，但中间的两个不是。

这是iGraph中的一个bug，还是我对k核/graph.coreness算法的理解中的一个错误？

Answer 1

根据我对k核的理解，所有连接并且至少有5度的8个节点不是都在一个值为5的k核中吗？然而，这8家公司中有两家的k核心价值分别为4和3.

不是的。k -核是图的一部分，如果迭代地删除所有度小于k的节点，就意味着如果一些节点的度由于其他节点的删除而下降到k以下，那么您也必须删除这些节点。剩下的k核是一个子图，所有节点都有至少k度。在您的特殊情况下，删除图形最左边的节点和删除最上面的节点(右上角)会降低5以下其他两个节点的度数，因此它们也会被移除。