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Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different…
The Colour Refinement algorithm is a classical procedure to detect symmetries in graphs, whose most prominent application is in graph-isomorphism tests. The algorithm and its generalisation, the Weisfeiler-Leman algorithm, evaluate local…
We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate…
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…
Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still…
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…
Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…
Graphlets are induced subgraph patterns and have been frequently applied to characterize the local topology structures of graphs across various domains, e.g., online social networks (OSNs) and biological networks. Discovering and computing…
Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the…
Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms…
There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…
Many applications require to learn, mine, analyze and visualize large-scale graphs. These graphs are often too large to be addressed efficiently using conventional graph processing technologies. Many applications have requirements to…
Graph representation learning aims at transforming graph data into meaningful low-dimensional vectors to facilitate the employment of machine learning and data mining algorithms designed for general data. Most current graph representation…
Analyzing the temporal behavior of nodes in time-varying graphs is useful for many applications such as targeted advertising, community evolution and outlier detection. In this paper, we present a novel approach, STWalk, for learning…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
The ability of graph neural networks (GNNs) to count homomorphisms has recently been proposed as a practical and fine-grained measure of their expressive power. Although several existing works have investigated the homomorphism counting…
Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…
Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say,…
We propose a learning framework for graph kernels, which is theoretically grounded on regularizing optimal transport. This framework provides a novel optimal transport distance metric, namely Regularized Wasserstein (RW) discrepancy, which…