Related papers: Asymmetry and structural information in preferenti…

Computing over compressed data combines the space saving of data compression with efficient support for queries directly on the compressed representation. Such data structures are widely applied in text indexing and have been successfully…

In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…

Let $G$ be a graph with a vertex set $V$. The graph $G$ is path-proximinal if there are a semimetric $d \colon V \times V \to [0, \infty[$ and disjoint proximinal subsets of the semimetric space $(V, d)$ such that $V = A \cup B$, and…

We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…

For the set of graphs with a given degree sequence, consisting of any number of $2's$ and $1's$, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of $m$-matchings. We find the…

We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…

We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

A graph $H$ is said to be common if the number of monochromatic labelled copies of $H$ in a red/blue edge colouring of a large complete graph is asymptotically minimized by a random colouring with an equal proportion of each colour. We…

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…

Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…

One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs…

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

We prove that for every $m\in \mathbb N$ and every $\delta\in (-m,0)$, the chromatic number of the preferential attachment graph $PA_t(m, \delta)$ is asymptotically almost surely equal to $m+1$. The proof relies on a combinatorial…

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…

For any fixed integer $R \geq 2$ we characterise the typical structure of undirected graphs with vertices $1, ..., n$ and maximum degree $R$, as $n$ tends to infinity. The information is used to prove that such graphs satisfy a labelled…

We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time…