# Oversquashing Meets Resistance: Theoretical Link

- Oversquashing is tightly bounded by effective resistance between nodes.
- The Jacobian norm quantifies how much one node's features influence another.
- Lower resistance = stronger influence, less squashing.

\(\left\| \frac{\partial h_u^{(r)}}{\partial x_v} \right\| \leq (2\alpha\beta)^r \frac{d_{\max}}{2} \left( \frac{2}{d_{\min}} \left( r+1+\frac{\mu^{r+1}}{1-\mu} \right) - R_{u,v} \right)\)
where `h_u^{(r)}` is the feature vector at node u after r layers, `x_v` is the initial feature at node v, `α` and `β` bound the Jacobians of the GNN functions, `d_min` and `d_max` are the minimum and maximum degrees of u and v, `μ` is the largest nontrivial eigenvalue of the normalized adjacency, and `R_{u,v}` is the effective resistance.