Consider the graph object in a d dimension space ($R^d$) so each node represents a vector of dimension d and we want to reweight the edges of the graph based on a gaussian kernel function. Let a gaussian kernel function be defined as $$ K(x_i,x_j)= e^{-\alpha*\left \| x_i-x_j \right \|^2} $$
where $x_i$ is a point in a $R^d$ space and we calculate the weight of ($x_i,x_j$) edge with function K.
The question that I want to address is I want to know that this function is a Lipshitz function or not.
I know the definition of Lipschitz continuous, but I don't know how to use it here. Has someone a hint?