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Since you mentioned shortest route, by network analysis I assume that you mean analysing the min and max lengths of a path through a given graph/network. The simplest shortest route algorithm is Dijkstra's algorithm and is as follows:

1. mark all nodes as unvisited, and set total length of each node as infinity, except the initial/starting node which should be marked 0 and current.

2. travel along the current node's shortest adjacent arcto an unvisited node.

3. add the arc's length and the previous node's total length to the current nodes total length, and then mark the current node as current and the previous node as visited.

4. repeat 2 and 3 until you reach your target node.

The algorithm for longest path is the same except in step two you follow the node's longest adjacent arc.

For the linear programming of this visit the related link below this answer.

Q: Network analysis by linear programming and shortest route?

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