Related papers: Edge corona product as an approach to modeling com…
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…
In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and…
We construct a generative network for Monte-Carlo sampling in lattice field theories and beyond, for which the learning of layerwise propagation is done and optimised independently on each layer. The architecture uses physics-informed…
Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
We provide an up-to-date view of the structure of the energy landscape of the low autocorrelation binary sequences problem, a typical representative of the $NP$-hard class. To study the landscape features of interest we use the local optima…
Connectivity is one of the central ideas in graph theory, especially when it comes to building fault-tolerant networks. A cutset $S$ of $G$ is defined to be the set of vertices in $G$ whose removal disconnects the graph. An $R_g$ cutset of…
Gene regulatory networks (GRN) are being studied with increasingly precise quantitative tools and can provide a testing ground for ideas regarding the emergence and evolution of complex biological networks. We analyze the global statistical…
Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We study the irreversible $k$-threshold process on corona-type graph products, including the corona product, the double corona product, and a generalized base-$b$ corona construction. Exact results are obtained for the irreversible…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
In this paper, we initiate a systematic study of generalized binomial edge ideals of whisker graphs by working within a substantially broader class of graphs. We extend the notion of generalized corona products, and through this enlarged…
Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have…
Deterministic complex networks that use iterative generation algorithms have been found to more closely mirror properties found in real world networks than the traditional uniform random graph models. In this paper we introduce a new,…
We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure…
Understanding the evolution of connectivity in spatiotemporal systems requires mathematical frameworks capable of encoding not only instantaneous interactions but also their cumulative causal structure. In this work, we introduce the…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…