Visualizing relationships between python packages


Using the github data on BigQuery and new force layout in d3 via the Verlet numerical integration I implemented graph visualization of relationships between 3500 most popular python packages.

You can see the app at You can:

  • Pass different package names as a query argument in the URL.
  • Scroll the page horizontally and vertically.
  • Click a node to open the pypi. Note that not all packages are on pypi.

Graph properties:

  • Each node is each python package found on github. Radius is calculated in DataFrame with nodes section.
  • For two packages A and B, weight of an edge is (\frac{ |A \cap B|}{min(|A|, |B|)})^2, where |A \cap B| is number of occurrences of packages A and B within the same file.
  • Edges with weight smaller than 0.33 are removed.
  • Algorithm searches for minimal energy state by the Verlet Integration according to simulation parameters.

Center contains mostly standard library and the most interesting things are on the outskirts.

See the screenshot of the numpy cluster:


Graph visualizations often lack actionable insights except looking cool. Types of insights you can use this for:

  • I have been exploring packages in the scientific python cluster a lot, and I found a few things I plan to use.
  • Use this to evaluate which web framework to use. You may think that django became too heavyweight or some other framework have dying community.
  • Find some interesting python use cases, like robotics cluster.

Revision history of this post is on github.

Analysis of specific clusters

Scientific python land

Unsurprisingly, it is centered on numpy. Many of scientific packages are in close proximity, like scipy, pandas, sklearn or matplotlib.

I have found package networkx and graph_tool in the nearby proximity, that I plan to use for analyzing data from this post.

You can see even division between statistics and machine learning, by sklearn being surrounded by packages like xgboost or theano.

Robotics land

Nearby to scientific python land there is a robotics land centered at rospy. Some computational geometry packages like shapely are nearby.

Web frameworks

Web frameworks are interesting:

  • It could be said that sqlalchemy is a center of web frameworks land.
  • Found nearby, there’s a massive and monolithic cluster for django.
  • Smaller nearby clusters for flask and pyramid.
  • pylons, lacking a cluster of its own, in between django and sqlalchemy.
  • Small cluster for zope, also nearby sqlalchemy
  • tornado got swallowed by the big cluster of standard library in the middle, but is still close to other web frameworks.
  • Some smaller web frameworks like gluon (web2py) or turbo gears ended up close to django, but barely visible and without clusters of their own.

Open stack land

Cloud computing, open stack and low level networking land centered at nova contain packages like oslo, nova, webob, neutron, ironic or netaddr.

Testing land

Centered on unittest. Some packages in the cluster are testfixtures or atomic-reactor.


Cluster for some gaming related libraries, is centered around pygame.

Potentials for further analysis

Other programming languages

Majority of the code is not specific to python. Only the first step, create a table with packages, is specific to python.

I had to do a lot of work on fitting the parameters in Simulation parameters to make the graph look good enough. I suspect that I would have to do similar fitting to each language, as each language graph would have different properties.

Probably majority of languages would have “heavy weight” center cluster that makes it hard to fit the parameters, so maybe removing the cluster like in described in Reduce an effect of a heavy weight center cluster could make algorithm more easily generalizeable to other languages.

Reduce an effect of a heavy weight center cluster

“Standard library” cluster in the center is very heavyweight and includes many packages. It is also the least interesting, as everyone knows those packages, so there is little insight to be gained.

Removing standard library could improve the quality of visualization. Removing just standard library is not easily generalizeable to other programming languages.

Removing the biggest cluster as detected by clustering algorithm from sklearn or networkx could work well. Alternatively, cluster nodes prior to visualization and let users hide some clusters from the browser.

Reduce an effect of heavy weight packages

In current visualization, big central packages like django, numpy, os and sys dominate the graph. I believe that they dominate some of the smaller, more relevant relationships between smaller packages.

I thought about replacing edge weight from (\frac{ |A \cap B|}{min(|A|, |B|)})^2 by (\frac{ |A \cap B|}{|A| * |B|})^2, but that could end up clustering packages by size rather than by common usage.

Search for “Alternatives to package X”, e.g. seaborn vs bokeh

For example, it would be interesting to cluster together all python data visualization packages.

Intuitively, such packages would be used in similar context, but would be rarely used together. They would have high correlation of their neighbor weights, but low direct edge. This would work in many situations, but there are some others it wouldn’t handle well. Example case it wouldn’t handle well:

  • sqlalchemy is an alternative to django built-in ORM.
  • django ORM is only used in django.
  • django ORM is not well usable in other web frameworks like flask.
  • other web frameworks make heavy use of flask ORM, but not django built-in ORM.

Therefore, django ORM and sqlalchemy wouldn’t have their neighbor weights correlated. I might got some ORM details wrong, as I don’t do much web dev.

networkx and graph_tool packages

Thanks to this visualization I have found about networkx and graph_tool packages. It have some niceties for analyzing graphs. I plan to take a look at package dependency data using those packages.

Within repository relationship

Currently, I am only looking at imports within the same file. It could be interesting to look at the same graph built using “within same repository” relationship.


Steps to reproduce

Extract data from BigQuery

Create a table with packages

Save to wide-silo-135723:github_clustering.packages_in_file_py:

      REGEXP_EXTRACT(line, r"^from ([a-zA-Z0-9_-]+).*import"),
      REGEXP_EXTRACT(line, r"^import ([a-zA-Z0-9_-]+)")))) AS package
    id AS id,
    LTRIM(SPLIT(content, "\n")) AS line,
    line CONTAINS "import")
HAVING LENGTH(package) > 0;

Table will have two fields – id representing the file and repeated field with packages in the single file. Repeated fields are like arrays – the best description of repeated fields I found.

This is the only step that is specific for python.

Verify the packages_in_file_py table

Check that imports have been correctly parsed out from some random file.

    GROUP_CONCAT(package, ", ") AS packages,
    COUNT(package) AS count
FROM [wide-silo-135723:github_clustering.packages_in_file_py]
WHERE id == "009e3877f01393ae7a4e495015c0e73b5aa48ea7"
packages count
distutils, itertools, numpy, decimal, pandas, csv, warnings, future, IPython, math, locale, sys 12

Generate graph edges

I will generate edges and save it to table wide-silo-135723:github_clustering.packages_in_file_edges_py.

  p1.package AS package1,
  p2.package AS package2,
  COUNT(*) AS count
FROM FLATTEN([wide-silo-135723:github_clustering.packages_in_file_top_py], package)) AS p1
FROM [wide-silo-135723:github_clustering.packages_in_file_top_py]) AS p2
ON ( ==

Top 10 edges:

    count AS count
FROM [wide-silo-135723:github_clustering.packages_in_file_edges_py]
WHERE package1 < package2
package1 package2 count
os sys 393311
os re 156765
os time 156320
logging os 134478
sys time 133396
re sys 122375
__future__ django 119335
__future__ os 109319
os subprocess 106862
datetime django 94111

Filter out irrelevant edges

Quantiles of the edge weight:

    GROUP_CONCAT(STRING(QUANTILES(count, 11)), ", ")
FROM [wide-silo-135723:github_clustering.packages_in_file_edges_py];
1, 1, 1, 2, 3, 4, 7, 12, 24, 70, 1005020

In my first implementation I filtered edges out based on the total count. It was not a good approach, as a small relationship between two big packages was more likely to stay than strong relationship between too small packages.

Create wide-silo-135723:github_clustering.packages_in_file_nodes_py:

  package AS package,
  COUNT(id) AS count
FROM [github_clustering.packages_in_file_top_py]
package count
os 1005020
sys 784379
django 618941
__future__ 445335
time 359073
re 349309

Create table packages_in_file_edges_top_py:

    edges.package1 AS package1,
    edges.package2 AS package2,
    edges.count / IF(nodes1.count  0.33
AND package1 <= package2;

Full results in google docs.

Process data with Pandas to json

Load csv and verify edges with pandas

import pandas as pd
import math

df = pd.read_csv(“edges.csv”)
pd_df = df[( df.package1 == “pandas” ) | ( df.package2 == “pandas” )]
pd_df.loc[pd_df.package1 == “pandas”,”other_package”] = pd_df[pd_df.package1 == “pandas”].package2
pd_df.loc[pd_df.package2 == “pandas”,”other_package”] = pd_df[pd_df.package2 == “pandas”].package1

df_to_org(pd_df.loc[:,[“other_package”, “count”]])

print “\n”, len(pd_df), “total edges with pandas”

other_package count
pandas 33846
numpy 21813
statsmodels 1355
seaborn 1164
zipline 684
11 more rows  

16 total edges with pandas

DataFrame with nodes

nodes_df = df[df.package1 == df.package2].reset_index().loc[:, [“package1”, “count”]].copy()
nodes_df[“label”] = nodes_df.package1
nodes_df[“id”] = nodes_df.index
nodes_df[“r”] = (nodes_df[“count”] / nodes_df[“count”].min()).apply(math.sqrt) + 5
nodes_df[“count”].apply(lambda s: str(s) + ” total usages\n”)

package1 count label id r
os 1005020 os 0 75.711381704
sys 784379 sys 1 67.4690570169
django 618941 django 2 60.4915169887
__future__ 445335 __future__ 3 52.0701286903
time 359073 time 4 47.2662138808
3460 more rows        

Create map of node name -> id

id_map = nodes_df.reset_index().set_index(“package1”).to_dict()[“index”]

print pd.Series(id_map).sort_values()[:5]

os            0
sys           1
django        2
__future__    3
time          4
dtype: int64

Create edges data frame

edges_df = df.copy()
edges_df[“source”] = edges_df.package1.apply(lambda p: id_map[p])
edges_df[“target”] = edges_df.package2.apply(lambda p: id_map[p])
edges_df = edges_df.merge(nodes_df[[“id”, “count”]], left_on=”source”, right_on=”id”, how=”left”)
edges_df = edges_df.merge(nodes_df[[“id”, “count”]], left_on=”target”, right_on=”id”, how=”left”)

print “\ndf and edges_df should be the same length: “, len(df), len(edges_df)

package1 package2 strength count_x source target id_x count_y id_y count
os os 1.0 1005020 0 0 0 1005020 0 1005020
sys sys 1.0 784379 1 1 1 784379 1 784379
django django 1.0 618941 2 2 2 618941 2 618941
__future__ __future__ 1.0 445335 3 3 3 445335 3 445335
os sys 0.501429793505 393311 0 1 0 1005020 1 784379
11117 more rows                  

df and edges_df should be the same length: 11122 11122

Add reversed edge

edges_rev_df = edges_df.copy()
edges_rev_df.loc[:,[“source”, “target”]] = edges_rev_df.loc[:,[“target”, “source”]].values
edges_df = edges_df.append(edges_rev_df)

package1 package2 strength count_x source target id_x count_y id_y count
os os 1.0 1005020 0 0 0 1005020 0 1005020
sys sys 1.0 784379 1 1 1 784379 1 784379
django django 1.0 618941 2 2 2 618941 2 618941
__future__ __future__ 1.0 445335 3 3 3 445335 3 445335
os sys 0.501429793505 393311 0 1 0 1005020 1 784379
22239 more rows                  

Truncate edges DataFrame

edges_df = edges_df[[“source”, “target”, “strength”]]

source target strength
0.0 0.0 1.0
1.0 1.0 1.0
2.0 2.0 1.0
3.0 3.0 1.0
0.0 1.0 0.501429793505
22239 more rows    

After running simulation in the browser, get saved positions

The whole simulation takes a minute to stabilize. I could just download an image, but there are extra features like pressing the node opens pypi.

Download all positions after the simulation from the javascript console:

var positions = bar (n) { return [, n.x, n.y]; })

According to d3 documentation, by setting parameter “fx” and “fy” of node we will set it’s fixed position.

pos_df = pd.read_json(“fixed-positions.json”)
pos_df.columns = [“id”, “x”, “y”]
nodes_df = nodes_df.merge(pos_df, on=”id”)

Truncate nodes DataFrame

# c will be collision strength
nodes_df[“c”] = pd.DataFrame([nodes_df.label.str.len() * 1.8, nodes_df.r]).max() + 5
nodes_df = nodes_df[[“id”, “r”, “label”, “c”, “x”, “y”]]

id r label c x y
0 75.711381704 os 80.711381704 158.70817237 396.074393369
1 67.4690570169 sys 72.4690570169 362.371142521 -292.138913114
2 60.4915169887 django 65.4915169887 526.471326062 1607.83507287
3 52.0701286903 __future__ 57.0701286903 1354.91212894 680.325432179
4 47.2662138808 time 52.2662138808 419.407448663 439.872927665
3460 more rows          

Save files to json

# Truncate columns
with open(“graph.js”, “w”) as f:
f.write(“var nodes = {}\n\n”.format(nodes_df.to_dict(orient=”records”)))
f.write(“var nodeIds = {}\n”.format(id_map))
f.write(“var links = {}\n\n”.format(edges_df.to_dict(orient=”records”)))

Draw a graph using the new d3 Verlet Integration algorithm

The physical simulation

Simulation uses the new velocity Verlet integration force graph in d3 v 4.0. Simulation takes about one minute to stabilize, so for viewing purposes I hard-coded the position of node after running simulation on my machine.

To re-run the simulation you can:

Simulation parameters

I have been tweaking simulation parameters for a while. Very dense “center” of the graph is in conflict with clusters on the edge of the graph.

As you may see in the current graph, nodes in the center sometimes overlap, while distance between nodes on the edge of a graph is big.

I got as much as I could from the collision parameter and increasing it further wasn’t helpful. Potentially I could increase gravity towards the center, but then some of the valuable “clusters” from edges of the graph got lumped into the big “kernel” in the center. The most promising approach at this point would be to try some ways of Reduce an effect of a heavy weight center cluster.

  • Attraction forces
    • Weight of edge between packages A and B: (\frac{ |A \cap B|}{min(|A|, |B|)})^2, with distance 30
    • Gravity towards center: 0.1
  • Repulsion forces
    • Repulsion between nodes: -400
    • Strength of nodes collision: 5

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