# Glossary

- The
**adjacency matrix** of a graph is the n x n matrix, where A(i,j) is 1 if (i,j) are connected and zero else.
- The
**characteristic length** of a graph is the average distance between two different points.
The median length is the median of the distances between to other points.
- A graph is
**connected** if any two points can be connected with a path
x(1),x(2),..,x(n) with (x(k),x(k+1)) in E.
- The
**diameter** of a network is the maximal distance between two nodes.
- A
**finite simple graph** G=(V,E) is a graph without multiple connections and without loops.
The set V is the set of **vertices** and the set E is the set of **edges**.
- Given a subset Y of the vertex set V of a graph G, it
**generates** a subgraph (Y,W), where W consists of all pairs (x,y)
with (x,y) in V.
- The
**degree** d(x) of a vertex is the number of vertices in the unit sphere S(x). The average degree is 2|E|/|V|.
- The
**Laplacian** of G is the matrix D-A, where D is the diagonal matrix containing the vertex degrees.
- The
**local clustering coefficient** of a vertex is the number of
edges in the unit sphere divided by B(n(x),2), where n(x) is the number of vertices in the unit sphere.
The **mean clustering coefficient** is the average of all the local clustering coefficient.
- The
**sphere** of a vertex x is the sub graph generated by all the vertices attached to x.
- The
**vertex distribution** of a graph gives the probability distribution of the degree function d(x).