Online user actions

This example reproduces a typical data science situation in an internet company. We start from a pandas DataFrame with online user actions, for instance for an online text editor: the user can create a page, edit it, or delete it. We want to construct and visualize a graph of the users highlighting collaborations on the same page/project.

import igraph as ig
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

Let’s start by preparing some toy data representing online users. Each row indicates a certain action taken by a user (e.g. click on a button within a website). Actual user data usually come with time stamp, but that’s not essential for this example.

action_dataframe = pd.DataFrame(
    [
        ["dsj3239asadsa3", "createPage", "greatProject"],
        ["2r09ej221sk2k5", "editPage", "greatProject"],
        ["dsj3239asadsa3", "editPage", "greatProject"],
        ["789dsadafj32jj", "editPage", "greatProject"],
        ["oi32ncwosap399", "editPage", "greatProject"],
        ["4r4320dkqpdokk", "createPage", "miniProject"],
        ["320eljl3lk3239", "editPage", "miniProject"],
        ["dsj3239asadsa3", "editPage", "miniProject"],
        ["3203ejew332323", "createPage", "private"],
        ["3203ejew332323", "editPage", "private"],
        ["40m11919332msa", "createPage", "private2"],
        ["40m11919332msa", "editPage", "private2"],
        ["dsj3239asadsa3", "createPage", "anotherGreatProject"],
        ["2r09ej221sk2k5", "editPage", "anotherGreatProject"],
    ],
    columns=["userid", "action", "project"],
)

The goal of this example is to check when two users worked on the same page. We choose to use a weighted adjacency matrix for this, i.e. a table with rows and columns indexes by the users that has nonzero entries whenever folks collaborate. First, let’s get the users and prepare an empty matrix:

users = action_dataframe["userid"].unique()
adjacency_matrix = pd.DataFrame(
    np.zeros((len(users), len(users)), np.int32),
    index=users,
    columns=users,
)

Then, let’s iterate over all projects one by one, and add all collaborations:

for _project, project_data in action_dataframe.groupby("project"):
    project_users = project_data["userid"].values
    for i1, user1 in enumerate(project_users):
        for user2 in project_users[:i1]:
            adjacency_matrix.at[user1, user2] += 1

There are many ways to achieve the above matrix, so don’t be surprised if you came up with another algorithm ;-) Now it’s time to make the graph:

g = ig.Graph.Weighted_Adjacency(adjacency_matrix, mode="plus")

We can take a look at the graph via plotting functions. We can first make a layout:

layout = g.layout("circle")

Then we can prepare vertex sizes based on their closeness to other vertices

vertex_size = g.closeness()
vertex_size = [10 * v**2 if not np.isnan(v) else 10 for v in vertex_size]

Finally, we can plot the graph:

fig, ax = plt.subplots()
ig.plot(
    g,
    target=ax,
    layout=layout,
    vertex_label=g.vs["name"],
    vertex_color="lightblue",
    vertex_size=vertex_size,
    edge_width=g.es["weight"],
)
plt.show()

Loops indicate “self-collaborations”, which are not very meaningful. To filter out loops without losing the edge weights, we can use:

g = g.simplify(combine_edges="first")

fig, ax = plt.subplots()
ig.plot(
    g,
    target=ax,
    layout=layout,
    vertex_label=g.vs["name"],
    vertex_color="lightblue",
    vertex_size=vertex_size,
    edge_width=g.es["weight"],
)
plt.show()