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For an arbitrary, fixed graph (pattern graph), we study the algorithmic complexity of counting homomorphisms, subgraph isomorphisms, and induced subgraph isomorphisms from the pattern graph to $n$-vertex, $d$-degenerate graphs as input.…

Data Structures and Algorithms · Computer Science 2025-11-07 Balagopal Komarath , Anant Kumar , Akash Pareek

In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…

Social and Information Networks · Computer Science 2020-10-28 Ryan A. Rossi , Nesreen K. Ahmed , Aldo Carranza , David Arbour , Anup Rao , Sungchul Kim , Eunyee Koh

Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…

Machine Learning · Computer Science 2026-05-08 Katharina Limbeck , Nadja Häusermann , Martin Carrasco , Guy Wolf , Bastian Rieck

For the first time we provide a succinct pattern matching index for arbitrary graphs that can be built in polynomial time, which requires less space and answers queries more efficiently than the one in [SODA 2021]. We show that, given an…

Data Structures and Algorithms · Computer Science 2021-11-09 Nicola Cotumaccio

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…

Statistical Mechanics · Physics 2009-11-10 Bo Söderberg

Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $\epsilon n$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from…

Combinatorics · Mathematics 2008-02-10 Itai Benjamini , Oded Schramm , Asaf Shapira

Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…

Physics and Society · Physics 2024-06-05 A. A. Snarskii

Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…

Signal Processing · Electrical Eng. & Systems 2020-06-16 Muhammad Asad Lodhi , Waheed U. Bajwa

This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…

Data Structures and Algorithms · Computer Science 2015-09-23 David Gibb , Bruce Kapron , Valerie King , Nolan Thorn

We study the problems of counting copies and induced copies of a small pattern graph $H$ in a large host graph $G$. Recent work fully classified the complexity of those problems according to structural restrictions on the patterns $H$. In…

Computational Complexity · Computer Science 2024-04-15 Marco Bressan , Leslie Ann Goldberg , Kitty Meeks , Marc Roth

This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…

Methodology · Statistics 2018-05-28 Pariya Behrouzi , Fentaw Abegaz , Ernst C. Wit

We consider the problem of maintaining a $(1-\epsilon)$-approximation to the densest subgraph (DSG) in an undirected multigraph as it undergoes edge insertions and deletions (the fully dynamic setting). Sawlani and Wang [SW20] developed a…

Data Structures and Algorithms · Computer Science 2022-10-07 Chandra Chekuri , Kent Quanrud

A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…

Combinatorics · Mathematics 2015-02-03 Guy Moshkovitz , Asaf Shapira

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

Methodology · Statistics 2011-07-15 Nanny Wermuth

Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomass\'e and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while…

We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…

Methodology · Statistics 2019-10-23 Cian Naik , François Caron , Judith Rousseau

Graph Neural Networks (GNNs) have been widely used for modeling graph-structured data. With the development of numerous GNN variants, recent years have witnessed groundbreaking results in improving the scalability of GNNs to work on static…

Machine Learning · Computer Science 2022-06-06 Yanping Zheng , Hanzhi Wang , Zhewei Wei , Jiajun Liu , Sibo Wang

We prove that if $G$ is a sparse graph --- it belongs to a fixed class of bounded expansion $\mathcal{C}$ --- and $d\in \mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these…

Discrete Mathematics · Computer Science 2020-03-10 Jaroslav Nešetřil , Patrice Ossona de Mendez , Michał Pilipczuk , Xuding Zhu

Dynamic networks reflect temporal changes occurring to the graph's structure and are used to model a wide variety of problems in many application fields. We investigate the design space of dynamic graph visualization along two major…

Human-Computer Interaction · Computer Science 2022-09-07 Velitchko Filipov , Alessio Arleo , Markus Bögl , Silvia Miksch

The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…

Data Structures and Algorithms · Computer Science 2023-11-01 Tuukka Korhonen , Wojciech Nadara , Michał Pilipczuk , Marek Sokołowski