Chapter 2- Graphs and networks

Question	Answer
A graph	consists of vertices(nodes) which are connected by edges(arcs).
A sub graph	is part of a graph
Weighted graph(network)	If a graph has a number associated with each edge(its weight).
The degree or valency(or order) of a vertex	is the number of edges incident to it.
A path	is a finite sequence of edges, such that the end vertex of one edge in the sequence is the start vertex of the next, and in which no vertex appears more than once.
A walk	is a path in which your are permitted to return to vertices more than once.
A cycle(circuit)	is a closed 'path', i.e. the end vertex of the last edge is the start vertex of the first edge.
Two vertices are connected if A graph is connected if	there is a path between them. all its vertices are connected.
A loop	is an edge that starts and finishes at the same vertex.
A simple graph	is one in which there are no loops and not more than one edge connecting any pair of vertices.
Digraph	If the edges of a graph have a direction associated with them they are known as directed edges.
A tree	is a connected graph with no cycles.
A spanning tree of a graph,G,	is a sub graph which includes all the vertices of G and is also a tree.
A bipartite graph	consists of two sets of vertices, X and Y. The edges only join vertices in X to vertices in Y, not vertices within a set.
A complete graph	is a graph in which every vertex is directly connected by an edge to each of the other vertices. If the graph has n vertices the connected graph is denoted Kn.
A complete bipartile graph( denoted Kr, s)	is a graph in which there are r vertices in set X and s vertices in set Y.
Isomorphic graphs	show the same information but are drawn differently.
An adjacency matrix	records the number of direct links between vertices.
A distance matrix	records the weights on the edges. Where there is no weight, this is indicated by'-'.

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Chapter 2- Graphs and networks

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	Created by Ben Geeman about 7 years ago