graphon signal

[[concept]]

Graphon signal

A graphon signal is defined as a function $\mathcal{X}:[0,1]\to \mathbb{R}$

NOTE

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

NOTE

We focus on signals in $L_2$, or “finite energy signals”$\mathcal{X}\in L_2([0,1])$: ${\int }_0^1|\mathcal{X}(u){|}^{2}du\le B<\infty$

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

dsg

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