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Results tagged with laplacian
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user 45250
The Laplacian matrix is the representation of a graph in matrix form.
12
votes
Line graphs called "graph derivatives": any intuition?
If one considers a graph $G=(V,E)$ and a function $f:V\to\mathbb{R}$, it makes sense to look at the finite differences $f(v_i)-f(v_j)$ for neighboring vertices $v_i,v_j\in V$ as a sort of discrete der …
- 3,065
2
votes
How to understand the combinatorial Laplacian $\Delta$ which is defined on the graph?
Fix a vertex $v$. Then
$$
\nabla F(uv) = c(u,v)\big(F(v)-F(u)\big)
$$
for $u$ adjacent to $v$. Now
\begin{align*}
\nabla\cdot\nabla F(v) &= \sum_{uv} c(v,u)\big(F(u)-F(v)\big)\\ &= -F(v)\left(\sum_u c …
- 3,065