The net is vast and infinite
- A Graph (G) is made up of a set V of vertices and a set E of edges.
- Another names for the vertices are nodes and another name for the edges is links.
- The order of the graph (|V|) is the number of vertices.
- The size of the graph (|E|) is the number of edges.
- A vertex is listed as letter on this page. Ex a graph contain the vertices a, b and c.
- A edge is listed as as the two vertices it connect. Ex (a,b) and (b,c).
- In a undirected graph the edge (a,b) = (b,a).
- A directed graph have edges that go in one direction from a source node to a destination node.
- A walk is a sequence of vertices. A walk is closed if the first vertex and the last are the same, and open if they are different.
- A open walk with no repeat vertices is known as a path.
- A closed walk with no repeat vertices is known as a cycle.
- A acyclic graph contains no cycles.
- The length of a walk is the number of edges.
- A acyclic graph is called a tree.
- A spanning tree of a graph is another graph that contains all the vertices and is a tree. If each edge has a length then the tree with the minimal sum of all the weights is called the minimum spanning tree.
- The degree of a vertex is the number of edges it has. Loops are counted twice.
- A vertex of degree 0 is a isolated vertex and one with degree 1 is a leaf.
- The total degree of a graph is the sum of degrees of all it's vertices.
- Two vertices a and b are called adjacent if they are connected by a edge.
- A graph is said to be a weighted graph if it's edges contains a value.
- A complete graph is a graph where there is a edge between every pair of vertices.
- Both the nodes and the edges can contain information.
- A graph can be said to be between sparse or dense. Sparse graph have few connections per node and dense graphs have many.
- If V contain n vertices then the Adjacency matrix of the graph is a n*n matrix where A[i,j] contain 1 if there is a edge (i,j). If no edge it contain 0. In a weighted graph it can contain the weight of the edge.
- The diagonal entries are zero if there is no loops.
- In a undirected graph the matrix is symmetric (A[i,j] = A[j,i]).
- In a undirected graph each matrix element can use one bit per entry.
- Adjacency matrix storage is O(V^2).
Search Algorithms : http://en.wikipedia.org/wiki/Book:Graph_Algorithms