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We consider the problem of obtaining unbiased estimates of group properties in social networks when using a classifier for node labels. Inference for this problem is complicated by two factors: the network is not known and must be crawled,…

Social and Information Networks · Computer Science 2018-07-26 George Berry , Antonio Sirianni , Nathan High , Agrippa Kellum , Ingmar Weber , Michael Macy

Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…

Physics and Society · Physics 2024-06-13 Shazia'Ayn Babul , Yu Tian , Renaud Lambiotte

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

Methodology · Statistics 2025-11-05 Yiou Li , Lulu Kang

We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…

Statistical Mechanics · Physics 2009-11-10 Bosiljka Tadic

Local convergence has emerged as a fundamental tool for analyzing sparse random graph models. We introduce a new notion of local convergence, color convergence, based on the Weisfeiler-Leman algorithm. Color convergence fully characterizes…

Discrete Mathematics · Computer Science 2025-10-27 Alexander Pluska , Sagar Malhotra

Graph Neural Networks (GNNs) are effective tools for graph representation learning. Most GNNs rely on a recursive neighborhood aggregation scheme, named message passing, thereby their theoretical expressive power is limited to the…

Machine Learning · Computer Science 2023-09-19 Dingmin Wang , Shengchao Liu , Hanchen Wang , Bernardo Cuenca Grau , Linfeng Song , Jian Tang , Song Le , Qi Liu

Twin-width is a graph parameter introduced in the context of first-order model checking, and has since become a central parameter in algorithmic graph theory. While many algorithmic problems become easier on arbitrary classes of bounded…

Combinatorics · Mathematics 2026-01-12 Irene Heinrich , Moritz Lichter , Klara Pakhomenko , Simon Raßmann

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…

Machine Learning · Computer Science 2026-05-25 Ping Xiong , Thomas Schnake , Michael Gastegger , Grégoire Montavon , Klaus-Robert Müller , Shinichi Nakajima

Applying machine learning to molecules is challenging because of their natural representation as graphs rather than vectors.Several architectures have been recently proposed for deep learning from molecular graphs, but they suffer from…

Machine Learning · Statistics 2020-09-15 Jaak Simm , Adam Arany , Edward De Brouwer , Yves Moreau

Graph is an important data representation which occurs naturally in the real world applications \cite{goyal2018graph}. Therefore, analyzing graphs provides users with better insights in different areas such as anomaly detection…

Machine Learning · Computer Science 2024-05-06 Elika Bozorgi , Saber Soleimani , Sakher Khalil Alqaiidi , Hamid Reza Arabnia , Krzysztof Kochut

We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…

Probability · Mathematics 2020-05-20 David Aldous , Russell Lyons

The Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a…

Discrete Mathematics · Computer Science 2025-10-29 Thomas Schneider , Pascal Schweitzer

We introduce the framework of Deep Weisfeiler Leman algorithms (DeepWL), which allows the design of purely combinatorial graph isomorphism tests that are more powerful than the well-known Weisfeiler-Leman algorithm. We prove that, as an…

Logic in Computer Science · Computer Science 2020-03-25 Martin Grohe , Pascal Schweitzer , Daniel Wiebking

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function…

We propose a Graph Neural Network with greater expressive power than commonly used GNNs - not constrained to only differentiate between graphs that Weisfeiler-Lehman test recognizes to be non-isomorphic. We use a graph attention network…

Machine Learning · Computer Science 2020-04-14 Stanisław Purgał

Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of…

Information Retrieval · Computer Science 2023-09-19 Xuheng Cai , Lianghao Xia , Xubin Ren , Chao Huang

Single particle tracking allows probing how biomolecules interact physically with their natural environments. A fundamental challenge when analysing recorded single particle trajectories is the inverse problem of inferring the physical…

In this paper, we relate a beautiful theory by Lov\'asz with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the Weisfeiler-Leman…

Data Structures and Algorithms · Computer Science 2018-05-23 Holger Dell , Martin Grohe , Gaurav Rattan

We present a novel mechanism to improve the accuracy of the recently-introduced class of graph random features (GRFs). Our method induces negative correlations between the lengths of the algorithm's random walks by imposing antithetic…

Machine Learning · Statistics 2023-05-23 Isaac Reid , Krzysztof Choromanski , Adrian Weller

This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…

Quantum Physics · Physics 2019-04-26 Simon Apers