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Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture…
This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space,…
Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model, where nodes randomly distributed on a…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
In heterogeneous graphs, we can observe complex structures such as tree-like or hierarchical structures. Recently, the hyperbolic space has been widely adopted in many studies to effectively learn these complex structures. Although these…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
Graph representation learning (GRL) has emerged as an effective technique for modeling graph-structured data. When modeling heterogeneity and dynamics in real-world complex networks, GRL methods designed for complex heterogeneous temporal…
Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…
We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed…
Hypergraphs serve as an effective model for depicting complex connections in various real-world scenarios, from social to biological networks. The development of Hypergraph Neural Networks (HGNNs) has emerged as a valuable method to manage…
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…
Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…
In the last decades, the study of models for large real-world networks has been a very popular and active area of research. A reasonable model should not only replicate all the structural properties that are observed in real world networks…
Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…
Graph analysis is a critical component of applications such as online social networks, protein interactions in biological networks, and Internet traffic analysis. The arrival of massive graphs with hundreds of millions of nodes, e.g. social…
Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings…
Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them…