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This folder contains the code for GraphWave, an algorithm for computing structural signatures for nodes in a network using heat spectral wavelets.This code folder is organized as follows:

• shapes/: contains the functions for generating (more or less) regular graphs and shapes
• performance_evaluation/: functions computing different metrics for assessing the quality of the embeddings generated by GraphWave
• test_perturbation_synthetic/: set of ipython notebooks for running the syntheticexperiments described in the paper.
• utils/: set of helper functions
• files:
  • characteristic_functions.py: functions for computing the characteristic functions.
  • graphwave.py: wrapper function for computing the embeddings.

GraphWave was written forPython 2.7 and requires the installation of the following Python libraries:

• networkx: allows easy manipulation and plotting of graph objects (more information in theNetworkx website).
• pyemd: module for computing Earth Mover distances (for trying out other distances between diffusion distributions. More information in thepyemd website)

Also, need standard packages:scipy, sklearn, seaborn for analyzing and plotting results.

Note: heat diffusion scaling wavelets can also be computed with the Graph Signal Processing toolboxpygsp (accessible through theEPFL website ), which, beyond structural similarities, has plenty of extremely useful features for handling signals on graphs.

A full example on how to use GraphWave is provided in the ''Using GraphWave.ipynb" of this directory.In a nutshell:

• input: nx (or pygsp) Graph structure
• compute the heat wavelets
• embed the distributions in Euclidean space using the characteristic function
• output: signatures, which can be used in one's favorite Machine Learning framework.

For a given graphG (of type pygsp or nx),GraphWave structural signatures can be simplycomputing by calling:

>from graphwave import graphwave>chi,heat_print, taus=graphwave_alg(G, 'automatic', verbose=False)

• Anonymous at this time

We would like to thank the authors ofstruc2vec for theopen access of the implementation of their method, as well asLab41 for its open-access implementation ofRolX.

This project is licensed under the MIT License - see theLICENSE.md file for details

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