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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:alsoKnownAs
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Laplacian matrix
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gptkbp:application
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gptkb:machine_learning
image segmentation
community detection
random walks on graphs
electrical networks
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gptkbp:appliesTo
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graphs
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gptkbp:definedIn
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L = D - A
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gptkbp:eigenvalues
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contain information about graph connectivity
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gptkbp:field
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graph theory
linear algebra
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gptkbp:generalizes
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normalized Laplacian
signless Laplacian
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gptkbp:heldBy
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matrix representation of a graph
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|
https://www.w3.org/2000/01/rdf-schema#label
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graph Laplacian
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gptkbp:introduced
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gptkb:Gustave_Kirchhoff
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gptkbp:introducedIn
|
1847
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gptkbp:location
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A is the adjacency matrix
D is the degree matrix
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gptkbp:number_of_zero_eigenvalues
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equals number of connected components
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gptkbp:property
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positive semi-definite
symmetric for undirected graphs
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gptkbp:relatedTo
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gptkb:Cheeger_inequality
gptkb:Kirchhoff's_theorem
gptkb:Fiedler_vector
algebraic connectivity
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gptkbp:smallest_eigenvalue
|
is zero
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gptkbp:usedFor
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gptkb:spectral_graph_theory
network analysis
clustering
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gptkbp:bfsParent
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gptkb:Laplacian
gptkb:higher-order_Cheeger_inequalities
gptkb:Normalized_Cuts
gptkb:Chebyshev_Spectral_Graph_Convolutional_Network
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gptkbp:bfsLayer
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7
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