Local Graph Clustering

Local Graph Clustering provides

methods that find local clusters in a given graph without touching the whole graph
methods that improve a given cluster
methods for global graph partitioning
tools to compute Network Community Profiles
scalable graph analytics on your laptop

The current version is 0.5.0 and it is appropriate for experts and intermediates. Contact information for any questions and feedback is given below.

Authors

Kimon Fountoulakis, email: kimon.fountoulakis at uwaterloo dot ca
Meng Liu, email: liu1740 at purdue dot edu
David Gleich, email: dgleich at purdue dot edu
Michael Mahoney, email: mmahoney at stat dot berkeley dot edu

Contributors

Chufeng Hu, email: chufeng dot hu at uwaterloo dot ca
Yuying Li, email: yuying at uwaterloo dot ca
Ben Johnson, email: bkj dot 322 at gmail dot com

List of applications and methods

Approximate PageRank
L1-regularized PageRank (solved using accelerated proximal gradient descent)
PageRank Nibble
Rounding methods for spectral embeddings
MQI
FlowImprove
SimpleLocal
Capacity Releasing Diffusion
Multiclass label prediction
Network Community Profiles
Global spectral partitioning
Find k clusters using local graph clustering
Graph partitioning using local graph clustering
Image segmentation using local graph clustering
Densest subgraph
Triangle clusters and vertex neighborhood metrics
Handy network drawing methods

Pipelines

Examples

All examples are in the notebooks folder.

Below is a simple demonstration from test.py in notebooks on how to improve spectral partitioning using flow-based methods from local graph clustering.

from localgraphclustering import *

import time
import numpy as np

# Read graph. This also supports gml and graphml format.
g = GraphLocal('./datasets/senate.edgelist','edgelist',' ')

# Call the global spectral partitioning algorithm.
eig2 = fiedler(g)

# Round the eigenvector
output_sc = sweep_cut(g,eig2)

# Extract the partition for g and store it.
eig2_rounded = output_sc[0]

# Conductance before improvement
print("Conductance before improvement:",g.compute_conductance(eig2_rounded))

# Start calling SimpleLocal
start = time.time()
output_SL_fast = SimpleLocal(g,eig2_rounded)
end = time.time()
print("running time:",str(end-start)+"s")

# Conductance after improvement
print("Conductance after improvement:",g.compute_conductance(output_SL_fast[0]))

output_SL = output_SL_fast[0]

Examples with visualization

For general examples with visualization using our built-in drawing methods, see the Jupyter notebook examples with visualization.

For comparisons of spectral- and flow-based methods with visualization see the Jupyter notebooks here and here.

For visual demonstration of algorithms that can improve a given seed set of nodes see the Jupyter notebook here.

Scalable graph analytics on your laptop

For examples using reasonably large graphs (100 million edges) on a 16GB RAM laptop please see the Jupyter notebook here.

Advanced examples

For advanced examples see the Jupyter notebook here.

Demonstration: social networks

Demonstration: bioinformatics networks

Presentation

When local graph clustering methods do not perform well?

In theory and in practice we have observed that the performance of local graph clustering methods depends on the magnitute of the conductance of the target cluster as well as the magnitute of the minimum conductance in the induced subgraph of the target cluster. Simply put, if the "internal connectivity" of the target cluster (the minimum conductance in the induced subgraph of the target cluster) is not stronger than the "external connectivity" (the conductance of the target cluster) then local graph clustering methods have poor performance in terms of finding the target cluster. For theoretical details please see Section 3 in the Capacity Releasing Diffusion for Speed and Locality paper. For extensive numerical experiments that demonstrate properties of challenging target clusters please see Section 4 in Capacity Releasing Diffusion for Speed and Locality as well as the supplementary material in the same link.

Installation

Clone the repo

Enter the folder using the termimal

Type in the terminal `python setup.py install`

Note that this package runs only with Python 3.

It can also be installed through pip:

pip3 install localgraphclustering

Import from Julia

In Julia, add the PyCall package:

Pkg.add("PyCall")
Update which version of Python that PyCall defaults to:

ENV["PYTHON"] = (path to python3 executable)

Pkg.build("PyCall")

(You can get the path to the python3 executable by just running "which python3" in the terminal.)
Make sure the PyPlot package is added in Julia. 
Import localgraphclustering by using:

using PyPlot

using PyCall

@pyimport localgraphclustering

You can now use any routine in localgraphluserting from Julia.

License

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

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