visualizing dynamic edges

I’ve been trying to find a a way to visualize dynamic paths, since I couldn’t find anything which solves my problem, I’m posting it here. I’m sorry if there is already a post.

I’ve a some tracks which are represented as graphs which are grow with time,

at time 0 there will be a node
at time 1 there will be two nodes and an edge
at time 2 three nodes and two edges and so on.

What is the best way to represent it so that it can be visualized as an animation to show how the path grows progressively.