Related papers: Cliques in High-Dimensional Geometric Inhomogeneou…
This paper studies the magnitude homology of graphs focusing mainly on the relationship between its diagonality and the girth. Magnitude and magnitude homology are formulations of the Euler characteristic and the corresponding homology,…
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its…
Dimensionality effects pose major challenges in high-dimensional and non-Euclidean data analysis. Graph-based two-sample tests and change-point detection are particularly attractive in this context, as they make minimal distributional…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
Heterogeneous graphs (HGs) are common in real-world scenarios and often exhibit heterophily. However, most existing studies focus on either heterogeneity or heterophily in isolation, overlooking the prevalence of heterophilic HGs in…
Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn, can affect the outcomes of…
Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous…
Like other social animals and biological systems, human groups constantly exchange information. Network models provide a way of quantifying this process by representing the pathways of information propagation between individuals. Existing…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the…
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…
We study cliques in graphs arising from quadratic forms where the vertices are the elements of the module of the quadratic form and two vertices are adjacent if their difference represents some fixed scalar. We determine structural…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
The performance of distributed averaging depends heavily on the underlying topology. In various fields, including compressed sensing, multi-party computation, and abstract graph theory, graphs may be expected to be free of short cycles,…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
Generative modeling of graphs with spatial structure is essential across many applications from computer graphics to spatial genomics. Recent flow-based generative models have achieved impressive results by gradually adding and then…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…