A unit-distance embedding is a drawing of a graph in which distinct vertices are represented by distinct points and all edges are straight line segments of unit length, with no restriction on intersections between their interiors (Harris 2007).
In this established usage, the word embedding has a geometric meaning: it refers to assigning points to vertices subject to the unit-distance conditions on edges. This differs from topological graph theory, where a graph embedding maps the entire graph injectively into a surface and permits edges to meet only at common endpoints. A unit-distance embedding with intersecting edge segments is therefore a valid geometric embedding in the first sense, but only a drawing rather than an embedding in the topological sense.
A graph possessing a unit-distance embedding in two dimensions is called a unit-distance graph. Since all its edges have the integer length 1, a unit-distance embedding is also an integral drawing. When the same drawing is a planar graph embedding, the graph is a matchstick graph.
