Related papers: Random graph approach to multifunctional molecular…
The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
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…
A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged…
Generating molecular graphs is a challenging task due to their discrete nature and the competitive objectives involved. Diffusion models have emerged as SOTA approaches in data generation across various modalities. For molecular graphs,…
We propose a combination of a variational autoencoder and a transformer based model which fully utilises graph convolutional and graph pooling layers to operate directly on graphs. The transformer model implements a novel node encoding…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This…
A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node…
A molecule's geometry, also known as conformation, is one of a molecule's most important properties, determining the reactions it participates in, the bonds it forms, and the interactions it has with other molecules. Conventional…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
Generating novel molecules with optimal properties is a crucial step in many industries such as drug discovery. Recently, deep generative models have shown a promising way of performing de-novo molecular design. Although graph generative…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…