Networks & Graphs (Leaving Cert Applied Maths): Flashcards

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Adjacency Matrices
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What is a matrix?

Rectangular arrangement of numbers in rows and columns

Matrix dimensions notation

m×nm \times n (m=rows, n=columns)

What does mm represent in matrix dimensions?

Number of rows

What does nn represent in matrix dimensions?

Number of columns

What is an adjacency matrix?

Square matrix showing connections in a graph/network

In adjacency matrix, what does 1 mean?

Vertices are connected

Rule for reading adjacency matrices

Lawn Tennis rule - read from left to top

What do rows show in adjacency matrix?

Connections FROM that vertex

What do columns show in adjacency matrix?

Connections TO that vertex

What is the shape of adjacency matrices?

Always square (same number of rows and columns)

Property of adjacency matrices for undirected graphs

Symmetrical about the main diagonal

What does AnA^n represent?

Number of walks of length nn between vertices

Is matrix multiplication commutative?

No, AB≠BAAB \neq BA in general

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