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

Mentions

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