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Graph
A set of nodes together with a set of edges.

Edge
Has a node at each end.

Loop
Edge with the same node at each end.

Degree (or order) of a node
Number of edges incident (attached) to it.

Simple graph
Graoh with no loops, no more than one edge connecting any pair of nodes.

Walk
Sequence of edges where the end of one edge is the beginning of the next.

Trail
Walk in which no edge is repeated.

Path
Trail in which no node is repeated.

Cycle
Closed path (end of last edge is start of first edge).

Hamiltonian cycle
Cycle which visits every node.

Connected graph
Paths exist between every pair of nodes (each node has a degree of at least one).

Tree
Simple connected graph with no cycles.

Digraph (directed graph)
Graph where at least one edge has a direction to it.

Complete graph
Simple graph, every pair of nodes is connected by an edge.

Incidence matrix
Matrix that represents a graph.

Isomorphic graphs
Two graphs that can be distorted into each other (have the same connections).

Planar graph
Graph where no edges cross.

Biparitie graph
Graph with two sets of nodes, each node connected to another node in the opposite set

