One of the definitions for a path in Graph theory is :
A path (of length r) in a graph G = (V,E) is a sequence $v_0,...,v_r ∈ V$ of vertices such that $v_{i-1} −v_i ∈ E$ for all $i = 1,...,r$
It might be a bit of a dumb question but I'm having a trouble understanding this notation.What does $v_{i-1} −v_i$ mean in this context? How can you subtract one vertex from another?
If you like to think about it easier, you can mentally replace that notation with the notation $(v_{i-1},v_{i}) \in E$. Then if $G$ is not a directed graph, $(v_{i-1},v_{i})$ is pair of vertices forming an edge. And if $G$ is a directed graph, $(v_{i-1},v_{i})$ is an ordered pair