Related papers: Real-World Networks are Low-Dimensional: Theoretic…
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…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
Graph Neural Networks (GNNs) have become a central tool for learning on graph-structured data, yet their applicability to real-world systems remains limited by key challenges such as scalability, temporality, directionality, data…
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…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
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…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…
Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…
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…
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…
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
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…
Convolutional neural networks (CNNs) leverage the great power in representation learning on regular grid data such as image and video. Recently, increasing attention has been paid on generalizing CNNs to graph or network data which is…
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…
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…