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Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…

Combinatorics · Mathematics 2025-08-29 Jorik Jooken

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-03 Miguel E. Coimbra , Alexandre P. Francisco , Luis Veiga

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…

Discrete Mathematics · Computer Science 2015-09-30 Kevin E. Bassler , Charo I. Del Genio , Péter L. Erdős , István Miklós , Zoltán Toroczkai

Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation…

Machine Learning · Computer Science 2023-01-11 Faezeh Faez , Negin Hashemi Dijujin , Mahdieh Soleymani Baghshah , Hamid R. Rabiee

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

Discrete Mathematics · Computer Science 2010-02-09 Shweta Bansal , Shashank Khandelwal , Lauren Ancel Meyers

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

Graph data structures are fundamental for studying connected entities. With an increase in the number of applications where data is represented as graphs, the problem of graph generation has recently become a hot topic. However, despite its…

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph…

Machine Learning · Computer Science 2019-06-03 Da Xu , Chuanwei Ruan , Kamiya Motwani , Evren Korpeoglu , Sushant Kumar , Kannan Achan

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

Social and Information Networks · Computer Science 2016-08-11 Salvador Aguiñaga , Rodrigo Palacios , David Chiang , Tim Weninger

We propose a new family of efficient and expressive deep generative models of graphs, called Graph Recurrent Attention Networks (GRANs). Our model generates graphs one block of nodes and associated edges at a time. The block size and…

Imbalanced classification on graphs is ubiquitous yet challenging in many real-world applications, such as fraudulent node detection. Recently, graph neural networks (GNNs) have shown promising performance on many network analysis tasks.…

Machine Learning · Computer Science 2021-06-08 Liang Qu , Huaisheng Zhu , Ruiqi Zheng , Yuhui Shi , Hongzhi Yin

How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…

Social and Information Networks · Computer Science 2016-06-06 Junming Shao , Qinli Yang , Jinhu Liu , Stefan Kramer

Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree…

Discrete Mathematics · Computer Science 2018-12-17 Geoffrey Sanders , Roger Pearce , Timothy La Fond , Jeremy Kepner

We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory…

Machine Learning · Computer Science 2017-12-13 Alexandre Hollocou , Julien Maudet , Thomas Bonald , Marc Lelarge

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

We use multiple measures of graph complexity to evaluate the realism of synthetically-generated networks of human activity, in comparison with several stylized network models as well as a collection of empirical networks from the…

Social and Information Networks · Computer Science 2020-02-25 Kiran Karra , Samarth Swarup , Justus Graham

The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…

Databases · Computer Science 2021-10-22 Matthias Hauck , Ismail Oukid , Holger Fröning

Generating large synthetic attributed graphs with node labels is an important task to support various experimental studies for graph analysis methods. Existing graph generators fail to simultaneously simulate the relationships between…

Social and Information Networks · Computer Science 2023-02-14 Seiji Maekawa , Yuya Sasaki , George Fletcher , Makoto Onizuka

Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…

Social and Information Networks · Computer Science 2018-02-02 Junpeng Zhu , Hui Li , Mei Chen , Zhenyu Dai , Ming Zhu

We present an approach to synthesizing new graph structures from empirically specified distributions. The generative model is an auto-decoder that learns to synthesize graphs from latent codes. The graph synthesis model is learned jointly…

Machine Learning · Computer Science 2020-06-05 Sohil Atul Shah , Vladlen Koltun
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