Related papers: Random hypergraphs and algorithmics
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
An essential goal in mechanistic interpretability to decode a network, i.e., to convert a neural network's raw weights to an interpretable algorithm. Given the difficulty of the decoding problem, progress has been made to understand the…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
In the binomial random graph $\mathcal{G}(n,p)$, when $p$ changes from $(1-\varepsilon)/n$ (subcritical case) to $1/n$ and then to $(1+\varepsilon)/n$ (supercritical case) for $\varepsilon>0$, with high probability the order of the largest…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We determine to within a constant factor the threshold for the property that two random k-uniform hypergraphs with edge probability p have an edge-disjoint packing into the same vertex set. More generally, we allow the hypergraphs to have…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…
We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…
Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…
We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…
Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…