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Pairwise Compatibility Graphs: A Survey

Tiziana Calamoneri, Blerina Sinaimeri
2016 SIAM Review  
A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists an edgeweighted tree T and two nonnegative real numbers d min and dmax such that each leaf u of T is a node of V and there is  ...  In this article, we survey the state of the art concerning this class of graphs and some of its subclasses.  ...  A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists a tree T , a positive edge-weight function w on T , and two nonnegative real numbers d min and d max , d min ≤ d max , such that  ... 
doi:10.1137/140978053 fatcat:b63dwsicgfa6ffuzauswrr3b3q

On Generalizations of Pairwise Compatibility Graphs [article]

Tiziana Calamoneri, Manuel Lafond, Angelo Monti, Blerina Sinaimeri
2022 arXiv   pre-print
A graph G is a PCG if there exists an edge-weighted tree such that each leaf of the tree is a vertex of the graph, and there is an edge { x, y } in G if and only if the weight of the path in the tree connecting  ...  Finally, we use a Ramsey theory argument to show that for any k, there exist graphs that are not in k-AND-PCG, and graphs that are not in k-OR-PCG.  ...  In this paper we focus on the second group and more specifically on the class of pairwise compatibility graphs (PCGs) [12, 31, 42] which is a generalization of the class of leaf power graphs.  ... 
arXiv:2112.08503v2 fatcat:crcyelbzaraejgqc2vgm436cjy

Graph and hypergraph colouring via nibble methods: A survey [article]

Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, Deryk Osthus
2021 arXiv   pre-print
This paper provides a survey of methods, results, and open problems on graph and hypergraph colourings, with a particular emphasis on semi-random 'nibble' methods.  ...  We also give a detailed sketch of some aspects of the recent proof of the Erdős-Faber-Lovász conjecture.  ...  a previous version of the survey was disproved in [37] .  ... 
arXiv:2106.13733v3 fatcat:5apaxr4x7vanbofnzdzjhnhsb4

A Survey on Graph Representation Learning Methods [article]

Shima Khoshraftar, Aijun An
2022 arXiv   pre-print
Graphs representation learning has been a very active research area in recent years.  ...  In this survey, we provide an overview of these two categories and cover the current state-of-the-art methods for both static and dynamic graphs.  ...  In [325] , a class compatibility matrix is added into GNNs to improve the performance of GNNs in graphs that heterophily exist.  ... 
arXiv:2204.01855v2 fatcat:e5p76ipn6jgkzkajvucrvsa55e

Minimal triangulations of graphs: A survey

Pinar Heggernes
2006 Discrete Mathematics  
This survey presents and ties together these results in a unified modern notation, keeping an emphasis on the algorithms.  ...  Any given graph can be embedded in a chordal graph by adding edges, and the resulting chordal graph is called a triangulation of the input graph.  ...  Given a graph G, let S be an arbitrary set of pairwise non-crossing minimal separators of G.  ... 
doi:10.1016/j.disc.2005.12.003 fatcat:3kyxcgffjja6zfkzucqoa6uwyu

Graph Summarization Methods and Applications: A Survey [article]

Yike Liu, Tara Safavi, Abhilash Dighe, Danai Koutra
2018 arXiv   pre-print
This survey is a structured, comprehensive overview of the state-of-the-art methods for summarizing graph data. We first broach the motivation behind, and the challenges of, graph summarization.  ...  Finally, we discuss applications of summarization on real-world graphs and conclude by describing some open problems in the field.  ...  (A,R)-compatible grouping.  ... 
arXiv:1612.04883v3 fatcat:fhg2g5eldfdgfkzoqdmbfl5er4

A survey of hereditary properties of graphs

Mieczysław Borowiecki, Izak Broere, Marietjie Frick, Peter Mihók, Gabriel Semanišin
1997 Discussiones Mathematicae Graph Theory  
In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs.  ...  The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure, is emphasized.  ...  If is a union compatible partial order, then (K a , ⊆) is a distributive lattice.  ... 
doi:10.7151/dmgt.1037 fatcat:qpxm2z2i6rhwra7lk42p2lg2au

Scene Graph Generation: A Comprehensive Survey [article]

Guangming Zhu, Liang Zhang, Youliang Jiang, Yixuan Dang, Haoran Hou, Peiyi Shen, Mingtao Feng, Xia Zhao, Qiguang Miao, Syed Afaq Ali Shah, Mohammed Bennamoun
2022 arXiv   pre-print
This survey will help readers to develop a better understanding of the current research status and ideas.  ...  Scene Graph Generation (SGG) refers to the task of automatically mapping an image into a semantic structural scene graph, which requires the correct labeling of detected objects and their relationships  ...  Methods, which are used to connect the detected visual relationships to form a scene graph, do not fall in the scope of this survey.  ... 
arXiv:2201.00443v2 fatcat:s4w7sdf6dndzneujly54srh5c4

Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey [article]

Chenqing Hua
2022 arXiv   pre-print
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures.  ...  In this survey, we broadly study the intersection of GNNs and PGMs.  ...  Table 1 . 1 measures the compatibility between class labels Y and a pair of hidden representations Summary of models of GNNs and PGMs in this survey.  ... 
arXiv:2206.06089v1 fatcat:twv6sh5f3ngkrjfiyoger6vuuq

A Survey of RDF Stores SPARQL Engines for Querying Knowledge Graphs [article]

Waqas Ali, Muhammad Saleem, Bin Yao, Aidan Hogan, Axel-Cyrille Ngonga Ngomo
2021 arXiv   pre-print
This survey paper provides a comprehensive review of techniques and systems for querying RDF knowledge graphs.  ...  To keep the survey self-contained, we also provide a short discussion on graph partitioning techniques used in the distributed setting.  ...  Both pairwise and multiway joins are supported using zig-zag joins that seek forward to the maximum compatible join value across the triple patterns.  ... 
arXiv:2102.13027v4 fatcat:phontczhbfcvdjt5y75n3hfcge

A Comprehensive Survey on Graph Neural Networks [article]

Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, Philip S. Yu
2019 arXiv   pre-print
In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields.  ...  We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and  ...  It is challenging to control the global properties of generated graphs, such as graph connectivity, validity, and node compatibility.  ... 
arXiv:1901.00596v4 fatcat:xxuchvawonhczay2sgjgzw5wgu

What is Event Knowledge Graph: A Survey [article]

Saiping Guan, Xueqi Cheng, Long Bai, Fujun Zhang, Zixuan Li, Yutao Zeng, Xiaolong Jin, Jiafeng Guo
2022 arXiv   pre-print
This paper provides a comprehensive survey of EKG from history, ontology, instance, and application views.  ...  Specifically, to characterize EKG thoroughly, we focus on its history, definition, schema induction, acquisition, related representative graphs/systems, and applications.  ...  above methods for temporal relation extraction only focus on pairwise decisions.  ... 
arXiv:2112.15280v2 fatcat:szx75hnmbjem3cyltefxybanai

Simplicial decompositions of graphs: a survey of applications

Reinhard Diestel
1989 Discrete Mathematics  
And indeed, while quite a few graph properties are compatible with attachment along a simplex (i.e. can be lifted from simplicial factors to the whole graph), simplicial decompositions do tend to leave  ...  We survey applications of simplicial decompositions (decompositions by separating complete subgraphs) to problems in graph theory.  ... 
doi:10.1016/0012-365x(89)90084-8 fatcat:n7g4dykpxnahzogrtopyf2nitq

A Survey of Graph Mining Techniques for Biological Datasets [chapter]

S. Parthasarathy, S. Tatikonda, D. Ucar
2010 Managing and Mining Graph Data  
We conclude this article with a discussion of the key results and identify some interesting directions for future research.  ...  In this article we survey the principal results in the field examining them both from the algorithmic contributions and applicability in the domain in question.  ...  In particular we survey the role played by frequent graph mining algorithms and motif discovery algorithms in this context.  ... 
doi:10.1007/978-1-4419-6045-0_18 dblp:series/ads/ParthasarathyTU10 fatcat:aeu53r3dbzd67d5whkjypv64uq

A Comprehensive Survey on Graph Anomaly Detection with Deep Learning [article]

Xiaoxiao Ma, Jia Wu, Shan Xue, Jian Yang, Chuan Zhou, Quan Z. Sheng, Hui Xiong, Leman Akoglu
2021 arXiv   pre-print
a single graph, or anomalous graphs in a database/set of graphs.  ...  In this survey, we aim to provide a systematic and comprehensive review of the contemporary deep learning techniques for graph anomaly detection.  ...  ., ANOS ND/ED/SGD) are not compatible with ANOS GD because they are dedicated to detecting anomalies in a single graph, whereas ANOS GD is directed at detecting graph-level anomalies.  ... 
arXiv:2106.07178v4 fatcat:efargsqnxndqbfqat2q5iz54u4
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