vierekkäisyysmatriisit

Vierekkäisyysmatriisit, also known as incidence matrices in English, are mathematical objects used to represent relationships between two sets of objects in graph theory and combinatorics. Typically, one set of objects forms the rows and the other forms the columns of the matrix. An entry in the matrix, usually a 0 or 1, indicates whether a relationship exists between the corresponding row object and column object.

In the context of graphs, a common use of incidence matrices is to represent the connections between vertices and edges. A vertex-edge incidence matrix would have rows representing vertices and columns representing edges. A '1' at the intersection of a vertex row and an edge column would signify that the vertex is an endpoint of that edge. Conversely, a '0' would indicate no such connection.

Incidence matrices can also be used to describe other types of relationships, such as the incidence of points and lines in geometry, or the participation of individuals in different events. The structure of an incidence matrix directly reflects the bipartite nature of the relationship being modeled. They are a fundamental tool for analyzing and manipulating relational data in various fields of mathematics and computer science.