Graph partition

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Multi-level methods

METIS Scikit-learn Eigenvectors LOBPCG Multigrid

6 related topics

Spectral partitioning and spectral bisection

Adjacency matrix Degree matrix Diagonal matrix Laplacian matrix Fiedler vector

6 related topics

Applications

Conductance Cheeger bound

2 related topics

Graph partition methods

Kernighan–Lin algorithm Fiduccia-Mattheyses algorithms Spectral clustering Eigendecomposition Graph Laplacian

5 related topics

Topics to explore

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Overview

Graph Graph (discrete mathematics)
Partitioning Partition of a set
VLSI
Partition problem
Buluc et al. (2013) Graph partition
Minimum cut
Maximum cut

Problem complexity

NP-hard
NP-complete
P=NP
Finite Element Model (FEM) Finite element method

Problem

Graph partition methods

Kernighan–Lin algorithm
Fiduccia-Mattheyses algorithms Fiduccia-Mattheyses algorithm
Spectral clustering
Eigendecomposition
Graph Laplacian

Multi-level methods

Spectral partitioning and spectral bisection

Applications

Conductance Conductance (graph)
Cheeger bound

Other graph partition methods

Hamiltonian Hamiltonian mechanics

Software tools

ARPACK

Advanced semantic analysis

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Map overview Semantic statistics

Nodes46

Edges45

Triples68

Avg. degree1.96

Density0.043478

Components1

How this topic connects Entity context

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Graph partition

Top relations

has method · 16

Graph partition → An, Each, Fiduccia-Mattheyses, Global, In, Kernighan, Laplacian, Lin, LOBPCG, METIS, One, Since, The, Their, There, Well-known

related to Problem complexity · 11

Graph partition → Even, FEM, Finite Element Model, Grids, However, NP, NP-complete, NP-hard, Solutions, Typically, When

related to Further reading · 10

Graph partition → Applications, Bichot, Charles-Edmond, Graph Partitioning, ISBN, ISTE, Optimisation, Patrick, Siarry, Wiley

related to Software tools · 8

Graph partition → Among, ARPACK, Karypis, Kumar, Laplacian, LOBPCG, METIS, ParMetis

related to Modularity and ratio-cut · 7

Graph partition → Additionally, Figure, For, Minimum, Modularity, The, This

related to Conductance · 5

Graph partition → Another, Conductance, Laplacian, The, The Cheeger

related to Spectral partitioning and spectral bisection · 5

Graph partition → D-A, Given, Now, Spectral, The Laplacian

is a · 1

Graph partition → reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups

related to Immunization · 1

Graph partition → Graph

Important terminology Word statistics

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Important terminology

graph partitioning partition problem edges cut spectral methods vertices number algorithm bisection using approximation approach one clustering original partitioned applications

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Graph partition	is a	reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups	0.90	text
trees	instance of	Even for special graph classes	0.80	text
grids	instance of	Even for special graph classes	0.80	text
no reasonable approximation algorithms exist	instance of	Even for special graph classes	0.80	text
unless P	instance of	Even for special graph classes	0.80	text
Graph partition	has method	Since	0.60	section
Graph partition	has method	There	0.60	section
Graph partition	has method	Well-known	0.60	section
Graph partition	has method	Kernighan	0.60	section
Graph partition	has method	Lin	0.60	section
Graph partition	has method	Fiduccia-Mattheyses	0.60	section
Graph partition	has method	Their	0.60	section

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Min side: 3

Research this topic

Explore this topic

Multi-level methods

Spectral partitioning and spectral bisection

Applications

Graph partition methods

Key facts & relationships

Topics to explore

Overview

Problem complexity

Problem

Graph partition methods

Multi-level methods

Spectral partitioning and spectral bisection

Applications

Other graph partition methods

Software tools

Advanced semantic analysis

Map overview Semantic statistics

Graph partition

How this topic connects Entity context

Graph partition

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges