iGraph - k-core graph.coreness 低估了一些核心
iGraph - k-core with graph.coreness underestimating some cores
我在 R 中使用 iGraph 计算一组 10 个节点的 k 核。其中8个节点相连，且度数大于等于5，另外两个节点的度数仅为3。
根据我对k核的理解，难道8个节点都相连，且度数至少为5的节点不应该都在一个值为5的k核中吗？然而，这 8 个中的两个被赋予 4 和 3 的 k 核心值。
请参阅下面的可重现图表：
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")
... 生成同一图的这张图像 (https://www.dropbox.com/s/unkkgodf8ppteyq/igraph.png?dl=0)，左侧显示度数，右侧显示 k 核。
基本上，左上角和右上角节点的度数和k-core应该都是3。其余的应该是5，但是中间的两个不是。
这是 iGraph 中的错误，还是我对 k-core/graph.coreness 算法的理解有误？
From my understanding of k cores, shouldn't the 8 nodes that are all connected, and that have a degree of at least 5 all be in a k-core with value 5? Two of these 8, are being given k-core value of 4 and 3 however.
没有。 k-core 是如果你删除所有度数小于 k、iteratively 的节点得到的图的一部分，这意味着如果由于移除了other节点，一些节点的度数低于k，你也必须移除这些节点。剩下的 k-core 是一个子图，其中所有节点的度至少为 k。在您的特定情况下，删除图形最左侧的节点并删除最上面的节点（在右上角）会将其他两个节点的度数降低到 5 以下 - 因此它们也会被删除。
我在 R 中使用 iGraph 计算一组 10 个节点的 k 核。其中8个节点相连，且度数大于等于5，另外两个节点的度数仅为3。
根据我对k核的理解，难道8个节点都相连，且度数至少为5的节点不应该都在一个值为5的k核中吗？然而，这 8 个中的两个被赋予 4 和 3 的 k 核心值。
请参阅下面的可重现图表：
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")
... 生成同一图的这张图像 (https://www.dropbox.com/s/unkkgodf8ppteyq/igraph.png?dl=0)，左侧显示度数，右侧显示 k 核。
基本上，左上角和右上角节点的度数和k-core应该都是3。其余的应该是5，但是中间的两个不是。
这是 iGraph 中的错误，还是我对 k-core/graph.coreness 算法的理解有误？
From my understanding of k cores, shouldn't the 8 nodes that are all connected, and that have a degree of at least 5 all be in a k-core with value 5? Two of these 8, are being given k-core value of 4 and 3 however.
没有。 k-core 是如果你删除所有度数小于 k、iteratively 的节点得到的图的一部分，这意味着如果由于移除了other节点，一些节点的度数低于k，你也必须移除这些节点。剩下的 k-core 是一个子图，其中所有节点的度至少为 k。在您的特定情况下，删除图形最左侧的节点并删除最上面的节点（在右上角）会将其他两个节点的度数降低到 5 以下 - 因此它们也会被删除。