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Glite Dictionary
➗ A math operator 📐 About Laplace operator 🔢 A graph matrix
Laplacian

Laplacian

9.9
A table of numbers that shows how nodes in a network connect
  • noun
  • /ləˈplæs.i.ən/
  • Specialized
: matriz laplaciana
  • In graph theory, the Laplacian helps identify clusters and reduces dimensions.
  • graph Laplacian

Examples

  • Is the graph Laplacian named the Laplacian because it has the connections to Laplace's equation?

  • Researchers use the Laplacian matrix to study the properties of complex graphs.

  • It's called the graph Laplacian and has a name and, and and a fame of its own.

  • Based on the discrete Laplacian distribution, the fitting result can be represented as 20: Formula omitted. See PDF.

    Academic text (2017)

  • The decomposition Eq. (11) is an expansion in eigenfunctions of the graph Laplacian of the hypercube, which is also known as a Walsh transform in computer science.

    Academic text (2018)

  • The graph Laplacian is essential for analyzing the connectivity of networks.

Surface Forms

Laplacian singular
Laplacians plural

Morphology

Laplacian = Laplace (semi-transparent) = Laplace + ian

Formally 'Laplace' + '-ian', but the specific sense 'Laplacian matrix' is a technical graph-theory usage requiring specialized knowledge.

Etymology

Laplacian in graph theory takes its name from the French mathematician Laplace and the ending -ian, meaning 'related to'. It is the matrix that does the same job for networks as the Laplace operator does for continuous spaces, so calling it the Laplacian shows it measures how values change across a graph.