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Represent a network in a matrix

DIFFICULTYstandardchallengeexam
QUESTION TYPEMix of allChange
Complete a partial matrix for an undirected network with loopsRead one entry for an undirected network with loopsComplete a partial matrix for an undirected network with parallel edgesRead one entry for an undirected network with parallel edgesNOWMix of allRecommended
Question 1 of 8

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A network for computers on an office network is shown below. Each line represents one two-way data link

Network. Vertices: [Laptop | Desktop | Printer | Server]. Connections: Laptop -- Desktop; Desktop -- Printer; Printer -- Server; Laptop -- Printer; Server -- Desktop; Printer -- PrinterLaptopDesktopPrinterServer

Use this vertex order for both the rows and the columns of \(M\): Laptop, Desktop, Printer, Server. Rows name the starting vertex and columns name the ending vertex

4 marks

Determine each missing connection count in \(M\)

Partly completed connection matrix \(M\)

Rows, in order: Laptop, Desktop, Printer, Server

Columns, in order: Laptop, Desktop, Printer, Server

\[M = \begin{bmatrix} 0 & 1 & 1 & 0 \\ 1 & m_{22} & 1 & 1 \\ 1 & 1 & m_{33} & m_{34} \\ 0 & 1 & m_{43} & 0 \end{bmatrix}\]