Related papers: Imaginary replica analysis of loopy regular random…
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…
We analyze maximum entropy random graph ensembles with constrained degrees, drawn from arbitrary degree distributions, and a tuneable number of 3-loops (triangles). We find that such ensembles generally exhibit two transitions, a clustering…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
Graph mining to extract interesting components has been studied in various guises, e.g., communities, dense subgraphs, cliques. However, most existing works are based on notions of frequency and connectivity and do not capture subjective…
For random systems subject to a constraint, the microcanonical ensemble requires the constraint to be met by every realisation ("hard constraint"), while the canonical ensemble requires the constraint to be met only on average ("soft…
We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
This work has two contributions. The first one is extending the Large Deviation Principle for uniform hyper-graphons from Lubetzky and Zhao \cite{lubetzky2015replica} to the multi-relational setting where each hyper-graphon can have…
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology…
In this paper we describe a triple correspondence between graph limits, information theory and group theory. We put forward a new graph limit concept called log-convergence that is closely connected to dense graph limits but its main…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
We study the spectral gap of the Erd\H{o}s--R\'enyi random graph through the connectivity threshold. In particular, we show that for any fixed $\delta > 0$ if $$p \ge \frac{(1/2 + \delta) \log n}{n},$$ then the normalized graph Laplacian of…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…