def animate_contraction(g, e, frames = 12, **kwds):

    v1, v2 = e

    if not g.has_edge(v1,v2):

        raise ValueError("Given edge not found on Graph")

    ls = []

    posd = g.get_pos()

    for j in range(frames):

        gp = Graph(g)

        posdp = dict(posd)

        p1 = posdp[v1]

        p2 = posdp[v2]

        posdp[v2] = [a*(frames-j)/frames + b*j/frames

                    for a,b in zip(p2,p1)]

​

        gp.set_pos(posdp)

        ls.append(plot(gp, **kwds))

    return ls

​

def animate_vertex_deletion(g, v, frames = 12, **kwds):

    kwds2 = dict(kwds)

    if 'vertex_colors' in kwds:

        cs = dict(kwds['vertex_colors'])

        for c, vs in kwds['vertex_colors'].items():

            if v in vs:

                vs2 = list(vs)

                vs2.remove(v)

                cs[c] = vs2

        kwds2['vertex_colors'] = cs

    else:

        kwds2 = dict(kwds)

    g2 = Graph(g)

    posd = dict(g.get_pos())

    del posd[v]

    g2.delete_vertex(v)

    g2.set_pos(posd)

    return [plot(g, **kwds),plot(g2, **kwds2)]*int(frames/2)

def animate_edge_deletion(g, e, frames = 12, **kwds):

    v1, v2 = e

    g2 = Graph(g)

    g2.delete_edge(e)

    return [plot(g, **kwds),plot(g2, **kwds)]*int(frames/2)

def animate_glide(g, pos1, pos2, frames = 12, **kwds):

    ls = []

    for j in range(frames):

        gp = Graph(g)

        pos = {}

        for v in gp.vertices():

            p1 = pos1[v]

            p2 = pos2[v]

            pos[v] = [b*j/frames + a*(frames-j)/frames

                        for a,b in zip(p1,p2)]    

        gp.set_pos(pos)

        ls.append(plot(gp, **kwds))

    return ls

def medio(p1, p2):

    return tuple((a+b)/2 for a,b in zip(p1, p2))

​

def new_color():

    return (0.1+0.8*random(), 0.1+0.8*random(), 0.1+0.8*random())

def animate_minor(g, m, frames = 12, pause = 50, step_time = 100):

    '''Crea una animación que muestra cómo un grafo tiene un menor m

    '''

    posd = dict(g.get_pos())

    posg = posd.values()

    posm = m.get_pos().values()

    xmax = max(max(x for x,y in posg), max(x for x,y in posm))

    ymax = max(max(y for x,y in posg), max(y for x,y in posm))

    xmin = min(min(x for x,y in posg), min(x for x,y in posm))

    ymin = min(min(y for x,y in posg), min(y for x,y in posm))

    dd = g.minor(m)

    #Set colors

    m_colors = dict((v,new_color()) for v in m.vertices())

    g_colors = dict((m_colors[k],vs) 

                        for k,vs in dd.items())

​

    extra_vs = (set(g.vertices()) - 

                set(v for vs in dd.values() 

                      for v in vs))

    g_colors[(0,0,0)] = list(extra_vs)

​

    #pics contains the frames of the animation 

    #no colors at the beggining   

    gg = Graph(g)

    pics = [plot(gg)]*frames

​

    #First: eliminate extra vertices

    for v in extra_vs:

        pics.extend(animate_vertex_deletion(gg, v, frames,

                            vertex_colors = g_colors))

        gg.delete_vertex(v)

        del posd[v]

        g_colors[(0,0,0)].remove(v)

    del g_colors[(0,0,0)]

    #Second: contract edges

    for color, vs in g_colors.items():

        while len(vs) > 1:

            for j in range(1, len(vs)):

                if gg.has_edge(vs[0], vs[j]):

                    break

            pics.extend(animate_contraction(gg, (vs[0], vs[j]), frames,

                                vertex_colors = g_colors))

            for v in gg.neighbors(vs[j]):

                gg.add_edge(vs[0],v)

            gg.delete_vertex(vs[j])

            del posd[vs[j]]

            gg.set_pos(posd)

            posd = dict(gg.get_pos())

            del vs[j]

​

    #Relabel vertices of m so that they match with those of gg

    m = Graph(m)

    dd0 = dict((k, vs[0])  

                  for k,vs in dd.items() )

    m.relabel(dd0)

​

    #Third: glide to position in m

    pos_m = m.get_pos()

    pos_g = gg.get_pos()

    pics.extend(animate_glide(gg, pos_g, pos_m, frames,

                                vertex_colors = g_colors))

    gg.set_pos(pos_m)

    #Fourth: delete redundant edges

    for e in gg.edges(labels = False):

        if not m.has_edge(e):

            pics.extend(animate_edge_deletion(gg, e, frames,

                                vertex_colors = g_colors))

            gg.delete_edge(*e)

​

    #And wait for a moment

    pics.extend([plot(gg, vertex_colors = g_colors)]*frames)

    return animate(pics, xmin = xmin - 0.1, xmax = xmax + 0.1, 

                         ymin = ymin - 0.1, ymax = ymax + 0.1)

​

graph_list = {'CompleteGraph4':graphs.CompleteGraph(4),

              'CompleteGraph5':graphs.CompleteGraph(5),

              'CompleteGraph6':graphs.CompleteGraph(6),

              'BipartiteGraph3,3':graphs.CompleteBipartiteGraph(3,3),

              'BipartiteGraph4,3':graphs.CompleteBipartiteGraph(4,3),

              'PetersenGraph':graphs.PetersenGraph(),

              'CycleGraph4':graphs.CycleGraph(4),

              'CycleGraph5':graphs.CycleGraph(5),

              'BarbellGraph(3,2)':graphs.BarbellGraph(3,2)

              }

@interact

def _(u1 = text_control(value='Does this graph'),

      g  = selector(graph_list.keys(), buttons = True,default='CompleteGraph4'),

      u2 = text_control(value='have a minor isomorphic to this other graph:'),

      m  = selector(graph_list.keys(), buttons = True,default='CycleGraph4'),

      u3 = text_control(value='''? If it has, show it to me, 

      with an animation with the following parameters'''),

      frames = slider(1,15,1,4, label = 'Frames per second'),

      step_time = slider(1/10,2,1/10,1, label = 'Seconds per step')):

    g = graph_list[g]

    m = graph_list[m]

    if g == m:

        html('<h3>Please select two different graphs</h3>')

        return

    try:

        a = animate_minor(g, m, frames = frames)

        a.show(delay=100*step_time/frames)

    except ValueError:

        html('''<h3>The first graph have <strong>NO</strong> minor isomorphic to the second</h3>''')