Networks & Matrices (Edexcel A-Level Further Mathematics): Flashcards

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Networks & Matrices
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Definition of network in graph theory

Graph where edges represent connections; may have weights (distances, costs, capacities)

Adjacency matrix rows/columns

Represent vertices

aija_{ij} when edge exists (adjacency matrix)

aij=1a_{ij} = 1

aija_{ij} when no edge (adjacency matrix)

aij=0a_{ij} = 0

aija_{ij} when edge exists (weighted matrix)

Weight of edge between ii and jj

aija_{ij} when no edge (weighted matrix)

aij=inftya_{ij} = infty

Symmetry in undirected graph adjacency matrix

aij=ajia_{ij} = a_{ji}

Diagonal zero in adjacency matrix meaning

No self-loop at that vertex

Drawing network: connect vertices for matrix entries

Non-zero entries

Writing weighted matrix: value for no connection

inftyinfty

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