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In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…

Machine Learning · Computer Science 2023-11-02 Gleb Bazhenov , Denis Kuznedelev , Andrey Malinin , Artem Babenko , Liudmila Prokhorenkova

Graph isomorphism, a classical algorithmic problem, determines whether two input graphs are structurally identical or not. Interestingly, it is one of the few problems that is not yet known to belong to either the P or NP-complete…

Data Structures and Algorithms · Computer Science 2024-10-01 Sourav Dutta , Arnab Bhattacharya

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance.…

Signal Processing · Electrical Eng. & Systems 2021-03-11 Samuel Rey , Antonio G. Marques

An $H$-graph is one representable as the intersection graph of connected subgraphs of a suitable subdivision of a fixed graph $H$, introduced by Bir\'{o}, Hujter and Tuza (1992). An $H$-graph is proper if the representing subgraphs of $H$…

Data Structures and Algorithms · Computer Science 2022-03-24 Deniz Ağaoğlu Çağırıcı , Petr Hliněný

Graph clustering, which aims to divide nodes in the graph into several distinct clusters, is a fundamental yet challenging task. Benefiting from the powerful representation capability of deep learning, deep graph clustering methods have…

Machine Learning · Computer Science 2023-09-13 Yue Liu , Jun Xia , Sihang Zhou , Xihong Yang , Ke Liang , Chenchen Fan , Yan Zhuang , Stan Z. Li , Xinwang Liu , Kunlun He

A general novel approach mapping discrete, combinatorial, graph-theoretic problems onto ``physical'' models - namely $n$ simplexes in $n-1$ dimensions - is applied to the graph equivalence problem. It is shown to solve this long standing…

Statistical Mechanics · Physics 2007-05-23 Vladimir Gudkov , Shmuel Nussinov

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

Physics and Society · Physics 2025-01-31 James Martin , Tim Rogers , Luca Zanetti

Nowadays, graph-structured data are increasingly used to model complex systems. Meanwhile, detecting anomalies from graph has become a vital research problem of pressing societal concerns. Anomaly detection is an unsupervised learning task…

Machine Learning · Computer Science 2021-03-29 Xuhong Wang , Baihong Jin , Ying Du , Ping Cui , Yupu Yang

A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the…

Data Structures and Algorithms · Computer Science 2016-06-02 Thomas E. Portegys

The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs $G$ and $H$, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list…

Discrete Mathematics · Computer Science 2016-11-03 Pavel Klavik , Dušan Knop , Peter Zeman

In this paper we study a natural generalization of both {\sc $k$-Path} and {\sc $k$-Tree} problems, namely, the {\sc Subgraph Isomorphism} problem. In the {\sc Subgraph Isomorphism} problem we are given two graphs $F$ and $G$ on $k$ and $n$…

Data Structures and Algorithms · Computer Science 2009-12-15 Fedor V. Fomin , Daniel Lokshtanov , Venkatesh Raman , B. V. Raghavendra Rao , Saket Saurabh

We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in…

Computational Complexity · Computer Science 2018-09-25 Markus Bläser , Balagopal Komarath , Karteek Sreenivasaiah

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

Machine Learning · Computer Science 2021-03-16 Konstantin Avrachenkov , Andrei Bobu , Maximilien Dreveton

In recent work by Johnson et al. (2022), a framework was described for the study of graph problems over classes specified by omitting each of a finite set of graphs as subgraphs. If a problem falls into the framework then its computational…

Computational Complexity · Computer Science 2025-03-17 Tala Eagling-Vose , Barnaby Martin , Daniel Paulusma , Siani Smith

The problem of out-of-distribution detection for graph classification is far from being solved. The existing models tend to be overconfident about OOD examples or completely ignore the detection task. In this work, we consider this problem…

Machine Learning · Computer Science 2022-06-23 Gleb Bazhenov , Sergei Ivanov , Maxim Panov , Alexey Zaytsev , Evgeny Burnaev

Switching is an operation on a graph that does not change the spectrum of the adjacency matrix, thus producing cospectral graphs. An important activity in the field of spectral graph theory is the characterization of graphs by their…

Combinatorics · Mathematics 2025-10-03 Aida Abiad , Nils Van de Berg , Robin Simoens

For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…

Machine Learning · Computer Science 2018-02-06 Caglar Aytekin , Francesco Cricri , Lixin Fan , Emre Aksu

Graphs are widely used to model complicated data semantics in many application domains. In this paper, two novel and efficient algorithms Fast-ON and Fast-P are proposed for solving the subgraph isomorphism problem. The two algorithms are…

Data Structures and Algorithms · Computer Science 2019-04-19 Mosab Hassaan , Karam Gouda

I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…

Data Structures and Algorithms · Computer Science 2010-03-24 Marco Nissen

Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods face challenges in consistently achieving satisfactory performance and often lack interpretability, which hinders our understanding of…

Machine Learning · Computer Science 2024-06-28 Yifei Yang , Peng Wang , Xiaofan He , Dongmian Zou