Description of the project, datasets and experimental results can be found at the following website: http://fragkiskos.me/projects/communities_sensitivity/

• Linux (and other Unix-like systems)
• Python 2.7.9 (Anaconda 2.2.0)
• python-igraph 0.7.1.post4 (containing all community detection algorithms except Spectral clustering and Metis)
• scipy 0.15.1
• networkx 1.9.1
• conda 3.10.0
• metis 0.1a0
• scikit-learn 0.15.2
• matplotlib 1.4.3
• numpy 1.9.2

• NetworksFromSNAP.py: script containing all functions needed to read the datasets (i.e., graphs), put them in iGraph/NetworkX or Metis format, extract the greatest connected component of each graph (GCC) and perturb the GCC using one of the perturbation strategies. It also contains the function METIS_Clustering that allows to use Metis algorithm to detect communities.

• Add_Noise.py: sciprt containing the functions used for graph perturbation: function configuration_model_perturbation (which is also the null model normally used in the definition of the modularity), function uniform_perturbation (Noise based on uniform perturbation (Erdos-Renyi G(n,e/n) model)), function preferential_perturbation (Noise based on preferential perturbation to high degree nodes (Chung-Lu model)).

• NCP_plot_for_paper.py: script allowing to produce the figure "NCP plot of a real-world network (CA-HEP-TH) using Infomap algorithm."

• Plot_and_save_NCP_charts.py: function allowing to produce the structural sensitivity plots for the community detection algorithms. It also produces plots of the distribution (CDF) of clusters' sizes as function of noise.

• normalized_laplacian_spectrum.py: function that return the eigenvalues of the Laplacian of the graph.

• NCP_plot.py: function computing the NCP plot of a graph. The NCP plot measures the quality of the best possible community in a large network, as a function of the community size. See Lekovec et al. 2008 : "Community Structure in Large Networks Natural Cluster Sizes and the Absence of Large Well-Defined Clusters".

• variation_of_information_score.py: function used to compute the VI score for Spectral and Metis algorithm (their output format, i.e. the community structure, differs from the ones of algorithms using Igraph format graphs).

• community_quality_NetworkX.py: script containing functions modularity and conductance scores.

• community_utils_NetworkX.py: utils used by community_quality_NetworkX.py.

• LAUNCHER_ALL_ALGOS_V3.py: produces the results using the CA-HEP-TH network as example

How to set the paprameters if the LAUNCHER_ALL_ALGOS_V3.py script:

• Which community detection algorithm? The choice is done by setting the boolean variables to True or False. Lines 30, 32, 34, 36, 39, 41, 43, 45 for Blondel Multilevel, FastGreedyMM, Infomap, LeadingEigenvectors, Walktrap, LabelPropag, Spectral clustering and Metis algos.

• Line 50 : it is important to set the right number of active algorithms in variable nb_active_algos (i.e., number of previous boolean variables set to True).

• Line 54 : chose the network by setting the variable network_name with the appropriate index number from the list network_name ('Email-Enron'=network_name[0] , 'CA-GrQc'=network_name[1] , 'CA-AstroPhys'=network_name[2] , 'Wiki-Vote'=network_name[3] , 'AS-Caida'=network_name[4], 'CA-HepTh'=network_name[5], 'P2P-GNutella'=network_name[6]).

• Line 62 : chose the perturbation model (ERP=noise_model[0], CLP=noise_model[1] or CONFIG=noise_model[2]).

• Line 64 : chose the perturabation type (Add or Delete edges. Note that for CONFIG model this parameter is not important).

• Line 66 to line 75 : noise levels. The user has only to set the intensity of the perturbation at lines 69 (for Delete type) and 72 (for Add type). For example, for the CA-HEP-TH network, we have set the following parameters for the different perturbation models:

  • ERP+Add => epsilon_values = [i * 0.285 for i in epsilon_valuesI] (line 72)
  • ERP+Delete => epsilon_values = [i * 475 for i in epsilon_valuesI] (line 69)
  • CLP+Add => epsilon_values = [i * 0.285 for i in epsilon_valuesI] (line 72)
  • CLP+Delete => epsilon_values = [i * 91.6 for i in epsilon_valuesI] (line 69)
  • Configuration model => nothing to do (line 75)

• Set directory paths in lines 79 to 87 (paths and directories from where we read the input datasets (graphs in .txt format), do conversions in format readable by iGraph/Metis and write results):

• Line 79 : source_path = ***put your own path***

• Line 81 : convert_path = ***put your own path*** + network_name + '_iGraphFormat.txt'

• Line 82 : convert_path_metis = ***put your own path*** + network_name + '_MetisFormat.txt'

• Line 84 : convert_path_P = ***put your own path*** + network_name + '_iGraphFormat_Perturbed.txt'

• Line 85 : convert_path_metis_P = ***put your own path*** + network_name + '_MetisFormat_Perturbed.txt'

• Line 87 : path_results = ***put your own path***

• Line 95 to line 113 : we declare variables that will store results.

• Line 104 : boolean variable ifSave that allows to save plots on the disk (always set to True)

• Community detection

• Line 123 to 272 : do clustering of original (unperturbed) graphs and compute metrics.

• Line 290 to 805 : do clustering of perturbed graphs and compute metrics.

• Plot results

• Line 814 to 968 : produces functional sensitivity plots for several community detection algorithms (NMI, VI, ARI, Modularity, and Number of clusters versus noise levels).

• Line 979 to 1023 : produces structural sensitivity plots for the community detection algorithms (as well as CDF of clusters' sizes as function of noise).