4 problems

Let $k$ denote the number of groups in the standard graph-clustering problem, corresponding to the case $d=2$. Decelle et al.'s computational-gap conjecture. A computational gap ex…

Let $G$ be a large graph with a block structure, or a structure close to a block structure. Suppose that a small subgraph is sampled and that only a small number of links from each…

Let $\mathrm{P}$ be a probability measure whose support is a union of compact topological connected components. For $T>0$, let $\mathcal C_T$ denote the connected components of the…

Let a generalized random or generalized quasi-random graph have $k\geq 2$ underlying clusters. Its normalized Laplacian spectrum has $k$ eigenvalues, including the zero eigenvalue,…