Related papers: Fast generation of complex networks with underlyin…
Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersection. The class of Helly graphs is the discrete analogue of the class of hyperconvex metric spaces. It is also known that every graph…
We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
We give two new approximation algorithms to compute the fractional hypertree width of an input hypergraph. The first algorithm takes as input $n$-vertex $m$-edge hypergraph $H$ of fractional hypertree width at most $\omega$, runs in…
While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
Social network analysis faces profound difficulties in sharing data between researchers due to privacy and security concerns. A potential remedy to this issue are synthetic networks, that closely resemble their real counterparts, but can be…
Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
We give a deterministic algorithm for computing a global minimum vertex cut in a vertex-weighted graph $n$ vertices and $m$ edges in $\widehat O(mn)$ time. This breaks the long-standing $\widehat \Omega(n^{4})$-time barrier in dense graphs,…
In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…
In this work we investigate the problem of estimating the percolation centrality of every vertex in a graph. This centrality measure quantifies the importance of each vertex in a graph going through a contagious process. It is an open…
Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden…
Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…
Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…