GkLinearOperator

java.lang.Object

org.drip.graph.adjacencymatrix.GkToR1

org.drip.graph.adjacencymatrix.GkLinearOperator

public abstract class GkLinearOperator
extends GkToR1

GkOperator implements the G^k Adjacency Linear Operator and its Norm/Spectral Radius. The References are:

Dunford, N., and J. Schwartz (1963): Linear Operators II: Spectral Theory: Self-adjoint Operators in the Hilbert Space Wiley Interscience Hoboken NJ
Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press Cambridge MA
Guo, J. M., Z. W. Wang, and X. Li (2019): Sharp Upper Bounds of the Spectral Radius of a Graph Discrete Mathematics 342 (9) 2559-2563
Lax, P. D. (2002): Functional Analysis Wiley Interscience Hoboken NJ
Wikipedia (2024): Spectral Radius https://en.wikipedia.org/wiki/Spectral_radius

Module = Computational Core Module
Library = Graph Algorithm Library
Project = Graph Optimization and Tree Construction Algorithms
Package = Adjacency Matrix Representation of Graph

Author:: Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor Description

GkLinearOperator(R1ToR1 vertexFunction, int k)
GkLinearOperator Constructor

Method Summary

Modifier and Type	Method	Description
`double`	`evaluate(Network<java.lang.Double> graphNetwork, java.lang.String vertexName)`	Evaluate the Value across the Specified Graph Vertex
`GuoWangLi2019Bound`	`guoWangLi2019SpectralRadiusUpperBound(Network<java.lang.Double> graphNetwork, int k)`	Compute the GuoWangLi2019Bound Instance
`abstract double`	`spectralRadius()`	Compute the Spectral Radius

Methods inherited from class org.drip.graph.adjacencymatrix.GkToR1

bounded, evaluate, norm, vertexFunction

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- GkLinearOperator
  
  public GkLinearOperator(R1ToR1 vertexFunction, int k) throws java.lang.Exception
  
  GkLinearOperator Constructor
  
  Parameters:
  
  vertexFunction - R¹ to R¹ Vertex Function
  
  k - Norm Exponent
  
  Throws:
  
  java.lang.Exception - Thrown if the Inputs are Invalid
Method Details
- evaluate
  
  public double evaluate(Network<java.lang.Double> graphNetwork, java.lang.String vertexName) throws java.lang.Exception
  
  Evaluate the Value across the Specified Graph Vertex
  
  Parameters:
  
  graphNetwork - Graph Network
  
  vertexName - Vertex Name
  
  Returns:
  
  Value across all the Graph Vertexes
  
  Throws:
  
  java.lang.Exception - Thrown if the Graph is Invalid
- guoWangLi2019SpectralRadiusUpperBound
  
  public GuoWangLi2019Bound guoWangLi2019SpectralRadiusUpperBound(Network<java.lang.Double> graphNetwork, int k)
  
  Compute the GuoWangLi2019Bound Instance
  
  Parameters:
  
  k - Guo, Wang, and Li (2019) k Parameter
  
  Returns:
  
  GuoWangLi2019Bound Instance
- spectralRadius
  
  public abstract double spectralRadius()
  
  Compute the Spectral Radius
  
  Returns:
  
  Spectral Radius