induced graphon signal

[[concept]]

Induced Graphon Signal

Let $(G_{n}, X_{n})$ be a graph signal. The induced graphon signal is defined as the pair $(W_{n}, X_{n})$ where $W_{n}$ is the induced graphon and

X_{n} (u) = \sum_{i = 1}^{n} [x_{n}]_{i} 1 (u \in I_{i})

Where $1$ is the indicator function and

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}

Example

Mentions

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Created 2025-03-26 ֍ Last Modified 2025-09-11