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AMENChar is a MATLAB library that characterizing (and possibly differentiating) attributes among different classes of subgraphs in an attributed graph. These attributes can be used to further study the differences in the two classes, such as differences in structure of communities or behavior of individuals.


For installation, you should add all files in the main directory to MATLAB's path. You can do that with opening MATLAB in the main directory and using:



You can see an example of the usage in ~/example/example.m. Below, we go through the example step by step.

  1. Load an attributed graph. You can see our datasets here.

    % Load a dataset
    load example\amazon-video.mat
  2. Find subgraphs of interest for your classes. Here, we use graph attributes to create classes. We first identify nodes with a specific attribute and then find local communities around those nodes. The resulting subgraphs are our subgraphs of interest. We finally remove attributes selected as classes from the pool of attributes to avoid trivial results.

    % Choose classes from features
    classes = {'animation', 'classics'};
    % Find class membership matrix (C) and 
    % remove the features selected as a class
    % You can use ANY other method to choose classes
    [C, F, F_label] = util_class(F, F_label, classes);
    % Load communities
    % You can use ANY algorithms to find any sorts of target subgraphs here.
    load example\coms.mat
    % (Optional) Filter attributes to only those that appear 
    % in selected communities to achieve higher speed.
    [F,F_label] = util_filterComFeatures(coms, F, F_label);

    NOTE: coms should be a MATLAB cell array of size <# of classes> x 1. Each cell is also a cell array with every row a vector of the IDs of nodes inside a target subgraph. Examine ~/example/coms.mat in MATLAB for more details.

  3. Find the attribute weights of the subgraphs.

    % Find attribute weights (Xs) and update attributes to those with
    % non-zero weight for at least ONE subgraph in either of classes
    [Xs, F_label] = main_getAmenWeights(A, F, F_label, classes, coms);
  4. Finally, partition and rank attributes for both classes.

    % Partition the attributes
    [part] = main_partition(Xs);
    % Sort attributes by their "utility" along with their labels
    [util, util_labels] = main_filterUtility(Xs, part, F_label);
  5. By printing the top 5 attributes for both classes, you will have the following results.

    'Animation Class'      'Classics Class'              
    'Kids & Family'        'Musicals & Performing Arts'
    '3-6 Years'            'Comedy'                    
    '7-9 Years'            'Musicals'                  
    '10-12 Years'          'Drama'                     
    'Warner Home Video'    'Mystery & Suspense'        

Alternate SWP Optimization

If you want to use our (faster) heuristics instead of the (1-1/e) approx. solution, open the file main_partition.m and change line [part, ~] = SWP_Amen(Xs); to either of the following:

  • [part, ~] = SWP_linear(Xs); for the Simplified heuristic with pre-normalized weights.
  • [part, ~] = SWP_topK(Xs, K) for only finding top-K attributes for each class.


If our datasets or our codes are useful in your research, we kindly ask you to cite the paper below:

	author = {Rezaei, Aria and Perozzi, Bryan and Akoglu, Leman},
	title = {Ties That Bind: Characterizing Classes by Attributes and Social Ties},
	booktitle = {Proceedings of the 26th International Conference on World Wide Web Companion},
	series = {WWW '17 Companion},
	year = {2017},
	isbn = {978-1-4503-4914-7},
	location = {Perth, Australia},
	pages = {973--981},
	numpages = {9},
	url = {},
	doi = {10.1145/3041021.3055138},
	acmid = {3055138},
	publisher = {International World Wide Web Conferences Steering Committee},
	address = {Republic and Canton of Geneva, Switzerland},
	keywords = {attributed graphs, community understanding, homophily, social networks, subspace discovery},


The optimization code for the Submodular Welfare Problem is provided by Andreas Krause here. If their code has been useful in your work, please cite them properly.


Finding characterizing attributes among different classes of subgraphs in an attributed graph







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