# Generalized network

Jump to: navigation, search

A network in which the flow that reaches the destination could be different from the flow that left the source. In the incidence matrix, instead of

$LaTeX: \left[ \begin{array}{crc}

 \ldots & \vdots & \ldots \\ \ldots & -1 & \ldots \\ \ldots & \vdots & \ldots \\ \ldots & +1 & \ldots \\ \ldots & \vdots & \ldots

\end{array} \right] \begin{array}{l} \leftarrow \mbox{ source row } (i) \\ \\ \\ \leftarrow \mbox{ destination row } (j) \end{array}$

we have

$LaTeX: \left[ \begin{array}{crc}

 \ldots & \vdots & \ldots \\ \ldots & -1 & \ldots \\ \ldots & \vdots & \ldots \\ \ldots & g & \ldots \\ \ldots & \vdots & \ldots

\end{array} \right] \begin{array}{l} \leftarrow \mbox{ source row } (i) \\ \\ \\ \leftarrow \mbox{ destination row } (j) \end{array}$

where $LaTeX: g > 0$. If $LaTeX: g < 1$, there is a loss; if $LaTeX: g > 1$, there is a gain.