Animations with graph-tool

The drawing capabilities of graph-tool (see draw module) can be harnessed to perform animations in a straightforward manner. Here we show some examples which uses GTK+ to display animations in an interactive_window, as well as offscreen to a file. The idea is to easily generate visualisations which can be used in presentations, and embedded in websites.

SIRS epidemics

Here we implement a simple SIRS epidemics on a network, and we construct an animation showing the time evolution. Nodes which are susceptible (S) are shown in white, whereas infected (I) nodes are shown in black. Recovered (R) nodes are removed from the layout, since they cannot propagate the outbreak.

The script which performs the animation is called animation_sirs.py and is shown below.

#! /usr/bin/env python
# -*- coding: utf-8 -*-

# This simple example on how to do animations using graph-tool. Here we do a
# simple simulation of an S->I->R->S epidemic model, where each vertex can be in
# one of the following states: Susceptible (S), infected (I), recovered (R). A
# vertex in the S state becomes infected either spontaneously with a probability
# 'x' or because a neighbour is infected. An infected node becomes recovered
# with probability 'r', and a recovered vertex becomes again susceptible with
# probability 's'.

# DISCLAIMER: The following code is definitely not the most efficient approach
# if you want to simulate this dynamics for very large networks, and/or for very
# long times. The main purpose is simply to highlight the animation capabilities
# of graph-tool.

from graph_tool.all import *
from numpy.random import *
import sys, os, os.path

seed(42)
seed_rng(42)

# We need some Gtk and gobject functions
from gi.repository import Gtk, Gdk, GdkPixbuf, GObject

# We will use the network of network scientists, and filter out the largest
# component
g = collection.data["netscience"]
g = GraphView(g, vfilt=label_largest_component(g), directed=False)
g = Graph(g, prune=True)

pos = g.vp["pos"]  # layout positions

# We will filter out vertices which are in the "Recovered" state, by masking
# them using a property map.
removed = g.new_vertex_property("bool")

# SIRS dynamics parameters:

x = 0.001    # spontaneous outbreak probability
r = 0.1      # I->R probability
s = 0.01     # R->S probability

# (Note that the S->I transition happens simultaneously for every vertex with a
#  probability equal to the fraction of non-recovered neighbours which are
#  infected.)

# The states would usually be represented with simple integers, but here we will
# use directly the color of the vertices in (R,G,B,A) format.

S = [1, 1, 1, 1]           # White color
I = [0, 0, 0, 1]           # Black color
R = [0.5, 0.5, 0.5, 1.]    # Grey color (will not actually be drawn)

# Initialize all vertices to the S state
state = g.new_vertex_property("vector<double>")
for v in g.vertices():
    state[v] = S

# Newly infected nodes will be highlighted in red
newly_infected = g.new_vertex_property("bool")

# If True, the frames will be dumped to disk as images.
offscreen = sys.argv[1] == "offscreen" if len(sys.argv) > 1 else False
max_count = 500
if offscreen and not os.path.exists("./frames"):
    os.mkdir("./frames")

# This creates a GTK+ window with the initial graph layout
if not offscreen:
    win = GraphWindow(g, pos, geometry=(500, 400),
                      edge_color=[0.6, 0.6, 0.6, 1],
                      vertex_fill_color=state,
                      vertex_halo=newly_infected,
                      vertex_halo_color=[0.8, 0, 0, 0.6])
else:
    count = 0
    win = Gtk.OffscreenWindow()
    win.set_default_size(500, 400)
    win.graph = GraphWidget(g, pos,
                            edge_color=[0.6, 0.6, 0.6, 1],
                            vertex_fill_color=state,
                            vertex_halo=newly_infected,
                            vertex_halo_color=[0.8, 0, 0, 0.6])
    win.add(win.graph)


# This function will be called repeatedly by the GTK+ main loop, and we use it
# to update the state according to the SIRS dynamics.
def update_state():
    newly_infected.a = False
    removed.a = False

    # visit the nodes in random order
    vs = list(g.vertices())
    shuffle(vs)
    for v in vs:
        if state[v] == I:
            if random() < r:
                state[v] = R
        elif state[v] == S:
            if random() < x:
                state[v] = I
            else:
                ns = list(v.out_neighbours())
                if len(ns) > 0:
                    w = ns[randint(0, len(ns))]  # choose a random neighbour
                    if state[w] == I:
                        state[v] = I
                        newly_infected[v] = True
        elif random() < s:
            state[v] = S
        if state[v] == R:
            removed[v] = True

    # Filter out the recovered vertices
    g.set_vertex_filter(removed, inverted=True)

    # The following will force the re-drawing of the graph, and issue a
    # re-drawing of the GTK window.
    win.graph.regenerate_surface(lazy=False)
    win.graph.queue_draw()

    # if doing an offscreen animation, dump frame to disk
    if offscreen:
        global count
        pixbuf = win.get_pixbuf()
        pixbuf.savev(r'./frames/sirs%06d.png' % count, 'png', [], [])
        if count > max_count:
            sys.exit(0)
        count += 1

    # We need to return True so that the main loop will call this function more
    # than once.
    return True


# Bind the function above as an 'idle' callback.
cid = GObject.idle_add(update_state)

# We will give the user the ability to stop the program by closing the window.
win.connect("delete_event", Gtk.main_quit)

# Actually show the window, and start the main loop.
win.show_all()
Gtk.main()

If called without arguments, the script will show the animation inside an interactive_window. If the parameter offscreen is passed, individual frames will be saved in the frames directory:

$ ./animation_sirs.py offscreen

These frames can be combined and encoded into the appropriate format. Here we use the mencoder tool from mplayer to combine all the frames into a single file with YUY format, and then we encode this with the WebM format, using vpxenc, so that it can be embedded in a website.

$ mencoder mf://frames/sirs*.png -mf w=500:h=400:type=png -ovc raw -of rawvideo -vf format=i420 -nosound -o sirs.yuy
$ vpxenc sirs.yuy -o sirs.webm -w 500 -h 400 --fps=25/1 --target-bitrate=1000 --good --threads=4

The resulting animation can be downloaded here, or played below if your browser supports WebM.

This type of animation can be extended or customized in many ways, by dynamically modifying the various drawing parameters and vertex/edge properties. For instance, one might want to represent the susceptible state as either or , depending on whether a neighbor is infected, and the infected state as . Properly modifying the script above would lead to the following movie:

The modified script can be downloaded here.

Dynamic layout

The graph layout can also be updated during an animation. As an illustration, here we consider a very simplistic model for spatial segregation, where the edges of the graph are repeatedly and randomly rewired, as long as the new edge has a shorter euclidean distance.

The script which performs the animation is called animation_dancing.py and is shown below.

#! /usr/bin/env python
# -*- coding: utf-8 -*-

# This simple example on how to do animations using graph-tool, where the layout
# changes dynamically. We start with some network, and randomly rewire its
# edges, and update the layout dynamically, where edges are rewired only if
# their euclidean distance is reduced. It is thus a very simplistic model for
# spatial segregation.

from graph_tool.all import *
from numpy.random import *
from numpy.linalg import norm
import sys, os, os.path

seed(42)
seed_rng(42)

# We need some Gtk and gobject functions
from gi.repository import Gtk, Gdk, GdkPixbuf, GObject

# We will generate a small random network
g = random_graph(150, lambda: 1 + poisson(5), directed=False)

# Parameters for the layout update

step = 0.005       # move step
K = 0.5            # preferred edge length

pos = sfdp_layout(g, K=K)  # initial layout positions

# If True, the frames will be dumped to disk as images.
offscreen = sys.argv[1] == "offscreen" if len(sys.argv) > 1 else False
max_count = 5000
if offscreen and not os.path.exists("./frames"):
    os.mkdir("./frames")

# This creates a GTK+ window with the initial graph layout
if not offscreen:
    win = GraphWindow(g, pos, geometry=(500, 400))
else:
    win = Gtk.OffscreenWindow()
    win.set_default_size(500, 400)
    win.graph = GraphWidget(g, pos)
    win.add(win.graph)

# list of edges
edges = list(g.edges())

count = 0

# This function will be called repeatedly by the GTK+ main loop, and we use it
# to update the vertex layout and perform the rewiring.
def update_state():
    global count

    # Perform one iteration of the layout step, starting from the previous positions
    sfdp_layout(g, pos=pos, K=K, init_step=step, max_iter=1)

    for i in range(100):
        # get a chosen edge, and swap one of its end points for a random vertex,
        # if it is closer
        i = randint(0, len(edges))
        e = list(edges[i])
        shuffle(e)
        s1, t1 = e

        t2 = g.vertex(randint(0, g.num_vertices()))

        if (norm(pos[s1].a - pos[t2].a) <= norm(pos[s1].a - pos[t1].a) and
            s1 != t2 and                      # no self-loops
            t1.out_degree() > 1 and           # no isolated vertices
            t2 not in s1.out_neighbours()):   # no parallel edges

            g.remove_edge(edges[i])
            edges[i] = g.add_edge(s1, t2)


    # The movement of the vertices may cause them to leave the display area. The
    # following function rescales the layout to fit the window to avoid this.
    if count % 1000 == 0:
        win.graph.fit_to_window(ink=True)
    count += 1

    # The following will force the re-drawing of the graph, and issue a
    # re-drawing of the GTK window.
    win.graph.regenerate_surface(lazy=False)
    win.graph.queue_draw()

    # if doing an offscreen animation, dump frame to disk
    if offscreen:
        pixbuf = win.get_pixbuf()
        pixbuf.savev(r'./frames/dancing%06d.png' % count, 'png', [], [])
        if count > max_count:
            sys.exit(0)

    # We need to return True so that the main loop will call this function more
    # than once.
    return True


# Bind the function above as an 'idle' callback.
cid = GObject.idle_add(update_state)

# We will give the user the ability to stop the program by closing the window.
win.connect("delete_event", Gtk.main_quit)

# Actually show the window, and start the main loop.
win.show_all()
Gtk.main()

This example works like the SIRS example above, and if we pass the offscreen parameter, the frames will be dumped to disk, otherwise the animation is displayed inside an interactive_window.

$ ./animation_dancing.py offscreen

Also like the previous example, we can encode the animation with the WebM format:

$ mencoder mf://frames/dancing*.png -mf w=500:h=400:type=png -ovc raw -of rawvideo -vf format=i420 -nosound -o dancing.yuy
$ vpxenc sirs.yuy -o dancing.webm -w 500 -h 400 --fps=100/1 --target-bitrate=5000 --good --threads=4

The resulting animation can be downloaded here, or played below if your browser supports WebM.