有同事在做图论吗？

skywm

因为做混沌同步，要用到图的Laplacian谱，有些知识不太明白，需要请教。

gghhjj

什么问题？几年前学过一点，简单的可能知道些

skywm

这是我在Yahoo Graph Group 中问的,可还没人回
Given a graph G(E,V), |V|=n,its Laplacian matrix L=D-A, the second
smallest eigenvalue Lambda_2 of L is called algebraic connectivity.
Assume X= (x1,...,xn) is the corresponding eigenvector of Lambda_2.
My Question is:
If |x1-x2| is the maximum among all difference of |xi-xj|,i,j=1,...n
can we deduce that vertices 1 and 2 have the longest path among all pair of vertices? Is the inverse true?

gghhjj

没太看明白你的问题，不好意思