Everything about Graph partition
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in multiprocessor computers, among others. Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see Buluc et al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Graph partitionA 5-minute orientation
- Skim a recent paper: Multiview Clustering: A Scalable and Parameter-Free Bipartite Graph Fusion MethodInfluential work since 2022
- Pick up a classic book: Graph PartitioningThe most-reprinted book on the subject
- Read the landmark paper: A generalization of the retention index system including linear temperature programmed gas—liquid partition chromatographyCited 5,572 times
- Go sideways: Graph Coarsening AlgorithmA closely related topic
- Go sideways: CutwidthA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A generalization of the retention index system including linear temperature programmed gas—liquid partition chromatography
The partition dimension of a graph
Restrictions of graph partition problems. Part I
Using PageRank to Locally Partition a Graph
The walk partition and colorations of a graph
Satisfactory graph partition, variants, and generalizations
Polygonal Clustering Analysis Using Multilevel Graph‐Partition
Graph partition problems into cycles and paths
🆕 Influential since 2022
Multiview Clustering: A Scalable and Parameter-Free Bipartite Graph Fusion Method
Tensorized Bipartite Graph Learning for Multi-View Clustering
Multi-view unsupervised feature selection with consensus partition and diverse graph
GraphEdge: Dynamic graph partition and task scheduling for GNNs computing in edge network
SDP-based bounds for graph partition via extended ADMM
📚 Books worth reading
- 📕Graph PartitioningCharles-Edmond Bichot, Patrick Siarry · 2011
- 📕On k-ary n-cubesWeizhen Mao · 1994
- 📕Organized CollapseDmitry N. Kozlov · 2020
- 📕Die optimale Zerlegung von Netzen und die Optimierung des Prozessverhaltens im AdressraumHerman Widjaja · 1979
Graph partitionningCharles-Edmond Bichot · 2011- 📕Combinatorial Reciprocity TheoremsMatthias Beck, Raman Sanyal · 2019
- 📕Topics in Hyperplane ArrangementsMarcelo Aguiar, Swapneel Mahajan · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Graph Coarsening Algorithm A Graph Coarsening Algorithm is a family of metaheuristic algorithms used to reduce the size and complexity of a large graph while preserving its key structural…
- Cutwidth In graph theory, the cutwidth of an undirected graph is the smallest integer k {\displaystyle k} with the following property: there is an ordering of the…
- Minimum k-cut In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph…
- Spectral clustering In multivariate statistics, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality…
- Hypergraph In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge…
- Maximum cut In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary…
- Cut (graph theory) In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one…
- Segmentation-based object categorization The image segmentation problem is concerned with partitioning an image into multiple regions according to some homogeneity criterion. This article is primarily…