Related papers: Message passing approach to analyze the robustness…

Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…

Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive…

The most prevalent class of neural networks operating on graphs are message passing neural networks (MPNNs), in which the representation of a node is updated iteratively by aggregating information in the 1-hop neighborhood. Since this…

Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…

Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message…

In the paper we consider a graph model of message passing processes and present a method verification of message passing processes. The method is illustrated by an example of a verification of sliding window protocol.

Graph neural networks have received increased attention over the past years due to their promising ability to handle graph-structured data, which can be found in many real-world problems such as recommended systems and drug synthesis. Most…

Bootstrap percolation is an often used model to study the spread of diseases, rumors, and information on sparse random graphs. The percolation process demonstrates a critical value such that the graph is either almost completely affected or…

Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the…

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…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

The message passing framework is the foundation of the immense success enjoyed by graph neural networks (GNNs) in recent years. In spite of its elegance, there exist many problems it provably cannot solve over given input graphs. This has…

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…

Graphs are the most ubiquitous data structures for representing relational datasets and performing inferences in them. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations.…

The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing…

Graph Neural Networks (GNNs) have demonstrated strong performance in graph mining tasks due to their message-passing mechanism, which is aligned with the homophily assumption that adjacent nodes exhibit similar behaviors. However, in many…

In many real-world network datasets such as co-authorship, co-citation, email communication, etc., relationships are complex and go beyond pairwise. Hypergraphs provide a flexible and natural modeling tool to model such complex…

Graph Neural Networks (GNNs) have become a prominent approach to machine learning with graphs and have been increasingly applied in a multitude of domains. Nevertheless, since most existing GNN models are based on flat message-passing…

Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences.…