max_cap_path

Scilab function
Last update : 25/04/2007

max_cap_path - maximum capacity path

### Calling Sequence

  `[p,cap] = max_cap_path(i,j,g)`

### Parameters

- `i,j` : integers, node numbers
- `g` : graph list
- `p` : row vector of integer numbers of the arcs of the path if it exists
- `cap` : value of the capacity of the path

### Description

`max_cap_path` returns the path with maximum capacity from node `i` to node `j` for the graph `g` if it exists and returns the empty vector `[]` otherwise.

The capacities of the edges are given by the element `edge_max_cap` of the graph list. If its value is not given (empty vector `[]` ), `max_cap_path` returns the empty vector `[]` . The capacities must be strictly positive, i.e negative capacities are considered as equal to 0 (no capacity at all).

### Examples

    ta=[1 1 2 2 2 3 4 5 5 7 8 8 9 10 10 10 11 12 13 13 13 14 15 16 16 17 17];
    he=[2 10 3 5 7 4 2 4 6 8 6 9 7 7 11 15 12 13 9 10 14 11 16 1 17 14 15];
    g=make_graph('foo',1,17,ta,he);
    g('node_x')=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642];
    g('node_y')=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301];
    show_graph(g);
    ma=edge_number(g);
    g('edge_max_cap')=int(rand(1,ma)*16)+5;
    [p,cap]=max_cap_path(1,14,g);
    edgecolor=1*ones(1,ma); edgecolor(p)=11*ones(p); g('edge_color')=edgecolor;
    x_message(['The maximum capacity is: '+string(cap);
               'Showing the corresponding path']);
    show_graph(g); show_arcs(p);