Graph Terminology

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Graphs Definition: a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges.

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Transcript of Graph Terminology

  • GraphsDefinition:

    a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges.

  • A vertex is a point where edges meetAn edge can start and end at the same vertex

  • A vertex is a point where edges meetAn edge can start and end at the same vertex

  • A vertex is a point where edges meetVertices are also known as nodesEdges are also known as arcs

  • A weight is a number associated with an edge

  • A weight is a number associated with an edgeThis could represent a distance, time or cost

  • A path runs from one vertex to another along edgesbut no vertex is passed through more than once

  • A path runs from one vertex to another along edgesbut no vertex is passed through more than once

  • A closed path returns to the start

  • A closed path returns to the startThis is also known as a circuit or cycle

  • In a connected graph it is possible to find a path between any two vertices:

  • This graph is not connected:

  • A tree is a connected graph of some vertices which contains no cycles

  • A tree is a connected graph of some vertices which contains no cycles

  • A spanning tree is a connected graph of all vertices which contains no cycles

  • The minimum spanning tree is the spanning tree with the least weightLength of this tree is 19

  • The minimum spanning tree is the spanning tree with the least weightCan you find the least weight?

  • The minimum spanning tree is the spanning tree with the least weightThe least weight is 15

  • The minimum spanning tree is the spanning tree with the least weightThe least weight is 15


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