Before revision: A unit disk graph G on a given set of points P in the plane is a geometric graph where an edge exists between two points p,q \in P if and only if |pq| \leq 1. A  subgraph G' of G is a k-hop spanner if and only if for every edge pq\in G, the topological shortest path between p,q in G' has at most k edges.
After revision: A unit disk graph G on a given set of points P in the plane is a geometric graph where an edge exists between two points p,q \in P if and only if |pq| \leq 1. A subgraph G' of G is a k-hop spanner if and only if for every edge pq\in G, there is a path between p,q in G' has at most k edges.