The term intersection number denotes several distinct numerical invariants in mathematics.
In graph theory, the graph intersection number is the smallest size of a set on which a graph has an intersection graph representation. Equivalently, it is the minimum number of cliques needed to cover all the edges of the graph.
For an association scheme or coherent configuration, an association
scheme intersection number 
counts the elements that
connect a pair in the relation 
through the relations 
and 
.
In differential topology, an algebraic intersection number is the signed count of the transversal intersection points of two oriented complementary-dimensional submanifolds. It depends only on the corresponding homology classes and defines an intersection pairing. On a surface, the geometric intersection number of two curves is the minimum number of intersection points among representatives of their isotopy classes.
In algebraic geometry, an intersection number is the degree of an intersection product of complementary-dimensional cycles, counted with intersection multiplicities. Self-intersection numbers, arithmetic intersection numbers, and intersection numbers of cohomology or tautological classes are variants of this usage.
In design theory, a block intersection number can mean a possible value of the number of points common to two distinct blocks, or a parameter recording the distribution of such values.
