Related papers: Convergence of Message Passing Graph Neural Networ…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained…
Network representation learning and node classification in graphs got significant attention due to the invent of different types graph neural networks. Graph convolution network (GCN) is a popular semi-supervised technique which aggregates…
Message passing is a core mechanism in Graph Neural Networks (GNNs), enabling the iterative update of node embeddings by aggregating information from neighboring nodes. Graph Convolutional Networks (GCNs) exemplify this approach by adapting…
Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph…
Message-passing graph neural networks (MPGNNs) dominate modern graph learning. Typical efforts enhance MPGNN's expressive power by enriching the adjacency-based aggregation. In contrast, we introduce an efficient aggregation over walk…
Networks and network processes have emerged as powerful tools for modeling social interactions, disease propagation, and a variety of additional dynamics driven by relational structures. Recently, neural networks have been generalized to…
In general, Graph Neural Networks(GNN) have been using a message passing method to aggregate and summarize information about neighbors to express their information. Nonetheless, previous studies have shown that the performance of graph…
The counting power of Message Passing Neural Networks (MPNN) has been the subject of many recent papers, showing that they can express logic that involves counting up to a threshold or more generally satisfy a linear arithmetic constraint.…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
Graph Convolutional Network (GCN) has experienced great success in graph analysis tasks. It works by smoothing the node features across the graph. The current GCN models overwhelmingly assume that the node feature information is complete.…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this…
Deep Graph Neural Networks struggle with oversmoothing. This paper introduces a novel, physics-inspired GNN model designed to mitigate this issue. Our approach integrates with existing GNN architectures, introducing an entropy-aware message…