## Improved reweighted graphs

In MatlabBGL 3.0, reweighted graphs were a pain to use. Now they are simple! We combine a structural matrix with a weight matrix. As(i,j)=1 if there is an edge between vertex i and j and A(i,j)=wij where wij is the weight of the edge between i and j.

As = cycle_graph(6,'directed',0); % compute a 6 node cycle graph A = As; % set all the weights to be one initially A(2,3) = 0; A(3,2) = 0; % make one edge have zero weight fprintf('Edges\n'); full(As) fprintf('Weights\n'); full(A)

Edges ans = 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 Weights ans = 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0

Note that As is given as the graph in the following call, not A!

[d pred] = shortest_paths(As,1,'edge_weight',edge_weight_vector(As,A)); d(3) % distance from vertex 1 to vertex 3 should be just 1!

ans = 1

## Graph layout algorithms

Sometimes, it's really nice to see a picture of your graph. The BGL implements a few graph layout algorithms and so these are now in MatlabBGL 4.0!

```
G = grid_graph(6,5);
X = kamada_kawai_spring_layout(G);
gplot(G,X,'.-');
```

```
G = grid_graph(6,5);
X = fruchterman_reingold_force_directed_layout(G);
gplot(G,X,'.-');
```

```
G = grid_graph(6,5);
X = gursoy_atun_layout(G);
gplot(G,X,'.-');
```

## Planar graph algorithms

The Boost Graph Library received a new suite of planar graph algorithms. These are now in MatlabBGL too.

A grid in the xy plane is a planar graph.

G = grid_graph(6,5); is_planar = boyer_myrvold_planarity_test(G)

is_planar = 1

Recall that K_5 (the clique on 5 vertices) is not a planar graph. Let's see what happens.

```
K5 = clique_graph(5);
is_planar = test_planar_graph(K5) % helpful wrapper
```

is_planar = 0

We can also draw planar graphs

G = grid_graph(6,5); X = chrobak_payne_straight_line_drawing(G); gplot(G,X,'.-'); % it looks a little different!

## New option syntax

You probably noticed that the "struct" command that permeated MatlabBGL calls before is gone in these examples. We've moved to a new option syntax that gives you the choice between the MatlabBGL struct style arguments and a list of key-value pairs

We'll look at spanning trees on the clique graph with 5 vertices. Using Prim's algorithm, the spanning tree we get depends on the root. We always get a star graph rooted at the vertex we pick as the root.

G = clique_graph(5);

Old style

full(mst(G,struct('root',5,'algname','prim')))

ans = 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0

New style

Just to make sure it works

full(mst(G,'root',1,'algname','prim'))

ans = 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0