Related papers: Message passing approach to analyze the robustness…

It is widely believed that information spread on social media is a percolation process, with parallels to phase transitions in theoretical physics. However, evidence for this hypothesis is limited, as phase transitions have not been…

Message-passing has proved to be an effective way to design graph neural networks, as it is able to leverage both permutation equivariance and an inductive bias towards learning local structures in order to achieve good generalization.…

In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…

We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous…

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…

In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…

Many real-world phenomena can be modeled as a graph, making them extremely valuable due to their ubiquitous presence. GNNs excel at capturing those relationships and patterns within these graphs, enabling effective learning and prediction…

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics.…

Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has difficulty sending information between distant nodes.…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…

Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at…

We study neural connectivity in cultures of rat hippocampal neurons. We measure the neurons' response to an electric stimulation for gradual lower connectivity, and characterize the size of the giant cluster in the network. The connectivity…

Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for…

Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the…

Recently, network coding technique has emerged as a promising approach that supports reliable transmission over wireless loss channels. In existing protocols where users have no interest in considering the encoded packets they had in coding…

The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties of the network. Indeed, the inverse of its leading eigenvalue is often used as an estimate for…

Existing message passing neural networks for heterogeneous graphs rely on the concepts of meta-paths or meta-graphs due to the intrinsic nature of heterogeneous graphs. However, the meta-paths and meta-graphs need to be pre-configured…

Graph neural networks (GNNs) and message passing neural networks (MPNNs) have been proven to be expressive for subgraph structures in many applications. Some applications in heterogeneous graphs require explicit edge modeling, such as…

This paper proposes a new measure of node centrality in social networks, the Harmonic Influence Centrality, which emerges naturally in the study of social influence over networks. Using an intuitive analogy between social and electrical…

Robustness in complex systems is of significant engineering and economic importance. However, conventional attack-based a posteriori robustness assessments incur prohibitive computational overhead. Recently, deep learning methods, such as…