bharathijeeva / structural-imbalance-notebook

Analyze the structural imbalance on a signed social network.

Structural Imbalance

This notebook explains the quantum processing unit (QPU) programming model used for calculating structural imbalance in signed social networks, and shows how to implement it.

The notebook has the following sections:

1. What is Structural Imbalance? defines and explains the structural imbalance problem.
2. Formulating the Problem shows how such optimization problems can be formulated for solution on a quantum computer.
3. A Toy Example codes a small structural imbalance problem to demonstrate the solution technique.
4. A Real-World Example applies the solution to the data sets of the Stanford Militants Mapping Project.

What is Structural Imbalance?

Social networks map relationships between people or organizations onto graphs, with the people/organizations as nodes and relationships as edges; for example, friends form a social network. Signed social networks map both friendly and hostile relationships by assigning to edges either positive or negative values. Such networks are said to be structurally balanced when they can be cleanly divided into two sets, with each set containing only friends, and all relations between these sets are hostile. The measure of structural imbalance or frustration for a signed social network, when it cannot be cleanly divided, is the minimum number of edges that violate the social rule, “the enemy of my friend is my enemy."

Finding a division that minimizes frustration is an NP-hard graph problem (it can be viewed as an expansion of the well-known maximum cut problem). This is an example of a broad class of optimization problems well-suited to solution on D-Wave systems. Other examples include protein folding, traffic flow optimization, job-shop scheduling, and many more.

Installation

You can run this example in the Leap IDE.

Alternatively, install requirements locally (ideally, in a virtual environment):

pip install -r requirements.txt

Usage

To enable notebook extensions¹:

jupyter contrib nbextension install --sys-prefix
jupyter nbextension enable toc2/main
jupyter nbextension enable exercise/main
jupyter nbextension enable exercise2/main
jupyter nbextension enable python-markdown/main

To run the notebook:

jupyter notebook

License

Released under the Apache License 2.0. See LICENSE file.

Footnotes

1. Leap's IDE, which runs VS Code, does not support all notebook extensions. Also, using the matplotlib package in interactive mode (with the %matplotlib ipympl code line) can degrade performance; it is recommended you switch that line to %matplotlib inline where noted in the notebook. ↩