Related papers: Message passing approach to analyze the robustness…
In this paper we offer a solution to a long-standing problem in the study of networks. Message passing is a fundamental technique for calculations on networks and graphs. The first versions of the method appeared in the 1930s and over the…
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
Message passing techniques on networks encompasses a family of related methods that can be employed to ascertain many important properties of a network. It is widely considered to be the state of the art formulation for networked systems…
Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…
Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…
Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
The Message-Passing Approach (MPA) is the state-of-the-art technique to obtain quasi-analytical predictions for percolation on real complex networks. Besides being intuitive and straightforward, it has the advantage of being mathematically…
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…
Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation…
Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain…
Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted…
The trust in the predictions of Graph Neural Networks is limited by their opaque reasoning process. Prior methods have tried to explain graph networks via concept-based explanations extracted from the latent representations obtained after…
There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight…
Hypergraphs are vital in modelling data with higher-order relations containing more than two entities, gaining prominence in machine learning and signal processing. Many hypergraph neural networks leverage message passing over hypergraph…