Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is… Expand

We propose a way of encoding sparse data using a “nonbacktracking” matrix and show that the corresponding spectral algorithm performs optimally for some popular generative models, including the stochastic block model.Expand

The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer… Expand

We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on nnodes and maximum degree dgiven observations.Expand

We prove that at the uniqueness threshold of the hardcore model on the regular tree, approximating the partition function becomes computationally hard on graphs of maximum degree $d$ for fugacity $\lambda_c(d) 0$.Expand

The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer… Expand

We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a=n and b=n for inter- and intra-block edge probabilities respectively.Expand

A striking conjecture of Decelle, Krzkala, Moore and Zdeborová [9], based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model.Expand

We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising model with arbitrary external field, it is NP-hard to approximate the partition function or approximately sample from the model on regular graphs when the model has non-uniqueness on the corresponding regular tree.Expand