Consists of points (called vertices or nodes) which are connected by lines (edges or arcs)
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Vertices
Points on a graph
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Nodes
Points on a graph
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Edges
Lines which connect the points on a graph
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Arcs
Lines which connect the points on a graph
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Weighted Graph
A graph which has a number associated with each edge (usually called its weight)
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Network
A graph which has a number associated with each edge (usually called its weight)
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Vertex Set
A list of vertices
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Edge Set
A list of edges
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Subgraph
A graph, each of whose vertices belongs to the original graph and each of whose edges belongs to the original graph. Basically it is part of the original graph
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Degree of a Vertex
The number of edges incident to it
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Valency of a Vertex
The number of edges incident to it
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Order of a Vertex
The number of edges incident to it
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Even Degree
When the degree of a vertex is even
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Path
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.
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Walk
A path in which you are permitted to return to vertices more than once.
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Cycle
A closed path, i.e. the end vertex of the last edge is the start vertex of the first edge.
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Circuit
A closed path, i.e. the end vertex of the last edge is the start vertex of the first edge.
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Connected
When there is a path between two vertices. A graph is connected if all its vertices are connected.
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Loop
An edge that starts and finishes at the same vertex
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Simple Graph
One in which there are no loops and does not have more than one edge connecting any pair of vertices.
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Directed Edges
When the edges of a graph have a direction associated with them.
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