def compute_count_execution_time(n=300, p=0.5, directed=False, num_iterations=10):
"""
Computes the average execution time (in seconds) of the triad motif counting
function on a random network of size n and connection probability p.
Arguments:
n => The number of nodes in the network.
p => The probability that any two nodes are connected.
directed => Whether or not the network is directed.
num_iterations => The number of function executions used to determine the
average execution time.
Returns:
A printable report showing average execution time and other network specs.
"""
# Define a list of execution times.
execution_times = []
# Run through simulations.
for _ in range(num_iterations):
# Build a standard random Erdos-Renyi network with the inputted size and connection
# probability (NOTE: this should not be included in the execution time).
network = build_erdos_renyi_network(n, p, directed=directed)
# Start the timer.
start_time = time.time()
# Execute the function.
count_triad_motifs(network, directed=directed)
# Append the final time.
execution_times.append(time.time() - start_time)
# Build a printable report to show the results.
report = "Network size: {0}\nConnection probability: {1}\nNumber of iterations: {2}\nDirected: {3}\nAverage execution time: {4:.3f} sec.".format(n, p, num_iterations, directed, np.mean(execution_times))
return report
def plot_motif_changes_over_randomization_steps(network, colormap="rainbow", rewiring_limit=None, title=None):
"""
Plots the convergence of motif counts over several randomization steps.
Arguments:
network => The input network.
colormap => A matplotlib colormap for giving different motif lines different colors.
rewiring_limit => An upper bound on the number of allowable edge rewirings (default set to 3 times
the number of edges in the network).
title => A custom plot title.
Returns:
Nothing, but shows a plot with motif counts converging over time.
"""
# Determine if the network is directed or not.
directed = nx.is_directed(network)
# Create a figure with hardcoded dimensions and one subplot.
fig = plt.figure(figsize=(16, 10))
ax = fig.add_subplot(1, 1, 1)
# Set some parameters specific to the directionality of the network.
if directed:
num_motifs = 13
else:
num_motifs = 2
# Count the motif before randomization.
starting_counts = count_triad_motifs(network)
# Keep a history of motif counts over time.
motif_count_history = starting_counts
# Keep a history of average motif counts over time (these are our y-values).
avg_motif_count_history = starting_counts
# Keep track of how many iterations have been performed.
num_rewirings_performed = 0
# Set a hard limit on the number than can be performed.
rewiring_limit = rewiring_limit or 3 * nx.number_of_edges(network)
while num_rewirings_performed < rewiring_limit:
# Randomly rewire a pair of edges in the network.
network = random_rewiring(network)
# Increment the counter.
num_rewirings_performed += 1
# Count the motifs in the slightly altered network.
new_motif_counts = count_triad_motifs(network)
# Add those counts to the motif history.
motif_count_history = np.vstack((motif_count_history, new_motif_counts))
# Determine the average motif counts over the current history.
avg_motif_counts = np.mean(motif_count_history, axis=0)
# Add that to the avg_motif_count_history stack of averages.
avg_motif_count_history = np.vstack((avg_motif_count_history, avg_motif_counts))
# Define x values.
X = np.arange(num_rewirings_performed + 1)
# Iterate through the extraction instances (synonymous with each color instance).
for motif in range(num_motifs):
# Parse all motif counts for a specific motif over time.
Y = avg_motif_count_history[:, motif]
# Plot the y-values with straight lines connecting them.
ax.plot(X, Y, label="Motif {}".format(motif + 1), linewidth=2.0)
# Add a legend for the lines in the plot.
ax.legend()
# Set the axis tick marks.
ax.xaxis.set_major_locator(ticker.MultipleLocator(50))
ax.xaxis.set_minor_locator(ticker.MultipleLocator(5))
ax.yaxis.set_major_locator(ticker.MultipleLocator(50))
ax.yaxis.set_minor_locator(ticker.MultipleLocator(5))
# Title and label the plot.
plt.title(title or "Motif Expression During Random Rewiring")
plt.xlabel("Number of Random Edge Rewirings")
plt.ylabel("Average Motif Counts")
# Show the resulting plot.
plt.show()
def plot_triad_motif_counts(network, title=None):
"""
Plots the triad motif counts for the input network.
Arguments:
network => The input network (directed or undirected).
title => A custom title for the plot (let's you specify which plot you're looking at).
Returns:
Nothing but produces a plot showing the triad motif counts.
"""
# Determine if the network is directed or not.
directed = nx.is_directed(network)
# Create a figure with hardcoded dimensions and one subplot.
fig = plt.figure(figsize=(16, 10))
ax = fig.add_subplot(1, 1, 1)
# Set some parameters specific to the directionality of the network.
if directed:
num_motifs = 13
ax.margins(0.05, 0.05)
motif_images = [OffsetImage(read_png("../project/static/directed_motif_1.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_2.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_3.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_4.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_5.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_6.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_7.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_8.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_9.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_10.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_11.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_12.png"), zoom=0.6),
OffsetImage(read_png("../project/static/directed_motif_13.png"), zoom=0.6)]
else:
num_motifs = 2
ax.margins(0.5, 0.5)
motif_images = [OffsetImage(read_png("../project/static/undirected_motif_1.png"), zoom=0.6),
OffsetImage(read_png("../project/static/undirected_motif_2.png"), zoom=0.6)]
# Define x values (integer for each motif).
X = np.arange(1, num_motifs + 1)
# Run the extraction code.
Y = count_triad_motifs(network)
# Plot the y-values with straight lines connecting them.
ax.scatter(X, Y, s=150)
# Define the x-y coordinate offsets for the images on the plot.
y_offset = -50
x_offset = 0
# Add each image to the plot.
for image, x in zip(motif_images, X):
ax.add_artist(AnnotationBbox(image, (x, ax.get_ylim()[0]), xybox=(x_offset, y_offset), xycoords='data',
boxcoords='offset points', frameon=False))
# Title and label the plot.
plt.title(title or "Triad Motif Counts")
plt.xlabel("Triad Motifs", labelpad=75)
plt.ylabel("Frequency")
# Set the y-axis tick marks.
ax.xaxis.set_major_locator(ticker.MultipleLocator(1))
ax.yaxis.set_minor_locator(ticker.MultipleLocator(5))
# Add extra spacing at the bottom of the plot for the images.
plt.subplots_adjust(bottom=0.2)
# Show the resulting plot.
plt.show()
