Generalized network

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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}
</p>
<pre>  \ldots & \vdots & \ldots \\
  \ldots & -1 & \ldots \\
  \ldots & \vdots & \ldots \\
  \ldots & +1 & \ldots \\
  \ldots & \vdots & \ldots
</pre>
<p>\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}
</p>
<pre>  \ldots & \vdots & \ldots \\
  \ldots & -1 & \ldots \\
  \ldots & \vdots & \ldots \\
  \ldots & g & \ldots \\
  \ldots & \vdots & \ldots
</pre>
<p>\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.


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