induced graphon

[[concept]]

induced graphon

Let $G_{n}$ be a graph with $n$ nodes. The graphon induced by $G_{n}$ is

W_{n} (u, v) = \sum_{i = 1}^{n} \sum_{j = 1}^{n} A_{i j} 1 (u \in I_{i}) \cdot 1 (v \in I_{j})

where $1$ is the indicator function and $I_{k}$ is defined as

I_{k} = {\begin{cases} [\frac{k - 1}{n}, \frac{k}{n}) 1 \leq k \leq n - 1 \\ [\frac{n - 1}{n}, 1] k = n \end{cases}

Symmetric "step function" on the unit square

Example

File
Davis-Kahan Theorem
convergence bound for graph convolutions
cut distance
eigenvalues of the induced graphon converge pointwise to the eigenvalues of the limit
graph sequence converges if and only if the induced graphon sequence converges
induced graphon signal
template graph
template graphs converge to the graphon
2025-03-24 graphs lecture 14
2025-03-26 lecture 15
2025-03-31 lecture 16
2025-04-02 lecture 17
2025-04-07 lecture 18

Created 2025-03-24 Last Modified 2025-05-13