All Questions

In Linial's presentation on SOME PROBLEMS AND RESULTS IN THE GEOMETRY OF GRAPHS, on slide 7, some relations of properties of graphs to the eigenvalues of their adjacency matrix are listed, e.g. if $G$...

Consider an $n$-node undirected graph $G = (V, E)$ equipped with weights $W$. Let $L$ be the weighted graph Laplacian matrix, i.e. $L_{ij} = -W_{(i,j)}$ for $(i,j)\in E$ and $L_{ii} = \sum_{j:(i,j)\in ...

This seems like a standard problem, but unable to find a solution online. Suppose we have two singular PSD matrices A and B with the following assumptions: $ 0 < x \leq ||A|| \leq y$ $ 0 < ||...

Assume the simple random walk $X$ on the graph $G(V,E)$, s.t. $G$ is simple, undirected, finite, connected and let $B \subset V$, s.t. $V\setminus B$ is connected. Let $\sigma_B$ be the quasi-...

It is well-known that a random graph a.e. has diameter 2. It is also well-known that the number of distinct eigenvalues of a graph is at least the diameter plus one. But what is known about the ...