Graph invariants | Mathematical chemistry
Szeged index
In chemical graph theory, the Szeged index is a topological index of a molecule, used in biochemistry. The Szeged index, introduced by Iván Gutman, generalizes the concept of the Wiener index introduced by Harry Wiener. The Szeged index of a connected graph G is defined as If e is an edge of G connecting vertices u and v, then we write e = uv or e = vu. For , let and be respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. Szeged index plays an important role in information theory. One way to measure a network structure is through the so-called topological indices. Szeged index has been shown to correlate well with numerous biological and physicochemical properties. (Wikipedia).
