Definition of metric space A set of elements with a distance function defined between any two elements of the set 4 properties of d:   Non-negativity:   Identity:   Symmetry:   Triangular inequality: Pseudometric space: Condition 2 (identity) is relaxed   Example: Number of vertices and edges of a graph Quasimetric space: Condition 3 (symmetry) is relaxed   Example: Time to walk from plain A to hill B Semimetric space: Condition 4 (triangular inequality) is relaxed   Example: Air fares on certain routes