graphon signal

[[concept]]

Graphon signal

A graphon signal is defined as a function

X : [0, 1] \to R

Note

contrast this with graph signals, which we defined as $x \in R^{n}$ .

Note

We focus on signals in $L_{2}$ , or "finite energy signals" $X \in L_{2} ([0, 1])$ :

\int_{0}^{1} | X (u) |^{2} d u \leq B < \infty

Analogously to the graphon, a graphon signal is {the limit of a convergent sequence of graph signals.} As when defining our cut distance for differently sized graphs, the graph signals may {not be comparable} since the dimension changes with the number of nodes. We solve this with an {induced graphon signal}

Review

#flashcards/math/dsg

Mentions

File
bandlimited graphon signal
convergence bound for graph convolutions
convergent sequence of graph signals
fixed coefficients yield the same spectral response for both graphon and graph convolutions
graph convolutions of bandlimited signals converge to the graphon convolution
graphon convolution
graphon fourier transform
graphon shift operator
graphon signal
inverse graphon fourier transform
lipschitz graph convolutions of graph signals converge to lipschitz graphon filters
spectral representation of graphon convolutions
spectral theorem for self-adjoint compact operators on Hilbert spaces
2025-03-26 lecture 15
2025-03-31 lecture 16
2025-04-02 lecture 17
2025-04-07 lecture 18

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