Calculating consensus partition in teneto

[balandongiv]

In the paper by Braun 2015, the measure the consensus partition from the modular allegiance matrix, and finally quantify the integration (See Fig 2 of the paper).

Correct me if I'm wrong, but is it correct, using teneto, this can be achieved as below

np.random.seed(10)
# Two graphlets templates with definite community structure
a = np.array([[1, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0], [
                 0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 1]])
b = np.array([[1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [1, 1, 1, 1, 0, 0], [
                 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 1]])
# Make into 4 time points
G = np.stack([a, a, b, b]).transpose([1, 2, 0])

# returns node,time array of community assignments
community_temporal = teneto.communitydetection.temporal_louvain(G, intersliceweight=0.1, n_iter=1)

# Calculate the allegiance
alleg = allegiance(community_temporal)


tnet_static = teneto.TemporalNetwork(from_array=np.tril(alleg),nodelabels=ch_names)

# Get the community/consensus partition
communities_static= teneto.communitydetection.temporal_louvain(tnet_static, intersliceweight=0.1, n_iter=1)

# Get the integration
icoeff = integration( communities_static)

[wiheto]

I do not fully understand the following code (because of variable names):

staticcommunities= teneto.communitydetection.temporal_louvain(G, intersliceweight=0.1, n_iter=1)

Does not look like this is "staticcommunities".

Also, the teneto communitydetection's intersliceweight is not necessarily in line with some other implementations. Something I've needed to look back on but never had the time.

But in essence this looks fine.

If you think something is wrong, let me know.

[balandongiv]

Thanks for the quick response. I had amended the variables names for clarity.

But, upon Googling, I found there is a dedicated function to measure 'consensus_iterative' written in Matlab from this weebly website.

function [S2, Q2, X_new3, qpc] = consensus_iterative(C)
%CONSENSUS_ITERATIVE     Construct a consensus (representative) partition
%using the iterative thresholding procedure
%
%   [S2 Q2 X_new3 qpc] = CONSENSUS_ITERATIVE(C) identifies a single
%   representative partition from a set of C partitions, based on
%   statistical testing in comparison to a null model. A thresholded nodal
%   association matrix is obtained by subtracting a random nodal
%   association matrix (null model) from the original matrix. The
%   representative partition is then obtained by using a Generalized
%   Louvain algorithm with the thresholded nodal association matrix.
%
%   NOTE: This code requires genlouvain.m to be on the MATLAB path
%
%   Inputs:     C,      pxn matrix of community assignments where p is the
%                       number of optimizations and n the number of nodes
%
%   Outputs:    S2,     pxn matrix of new community assignments
%               Q2,     associated modularity value
%               X_new3, thresholded nodal association matrix
%               qpc,    quality of the consensus (lower == better)
%               
%
%   Bassett, D. S., Porter, M. A., Wymbs, N. F., Grafton, S. T., Carlson,
%   J. M., & Mucha, P. J. (2013). Robust detection of dynamic community
%   structure in networks. Chaos: An Interdisciplinary Journal of Nonlinear
%   Science, 23(1), 013142.

npart = numel(C(:,1)); % number of partitions
m = numel(C(1,:)); % size of the network

% initialize
C_rand3 = zeros(size(C)); % permuted version of C
X = zeros(m,m); % Nodal association matrix for C
X_rand3 = X; % Random nodal association matrix for C_rand3

%% NODAL ASSOCIATION MATRIX

% try a random permutation approach
for i = 1:npart;
    pr = randperm(m);
    C_rand3(i,:) = C(i,pr); % C_rand3 is the same as C, but with each row permuted
end

% Calculate the nodal association matrices X and
% X_rand3
for i = 1:npart;
    ii=i
    tic
    for k = 1:m
        for p = 1:m;
            % element (i,j) indicate the number of times node i and node j
            % have been assigned to the same community
            if isequal(C(i,k),C(i,p))
                X(k,p) = X(k,p) + 1;
            else
                X(k,p) = X(k,p) + 0;
            end
            
            % element (i,j) indicate the number of times node i and node j
            % are expected to be assigned to the same community by chance
            if isequal(C_rand3(i,k),C_rand3(i,p))
                X_rand3(k,p) = X_rand3(k,p)+1;
            else
                X_rand3(k,p) = X_rand3(k,p)+ 0;
            end
        end
    end
    toc
end

%% THRESHOLDING
% keep only associated assignments that occur more often than expected in
% the random data
X_new3 = zeros(m,m);
X_new3(X>max(max(triu(X_rand3,1)))) = X(X>max(max(triu(X_rand3,1))));

%% GENERATE THE REPRESENTATIVE PARTITION
% recompute optimal partition on this new matrix of kept community
% association assignments
for i = 1:npart;
    ii=i
    [S2(i,:) Q2(i)] = multislice_static_unsigned(X_new3,1);
end

% define the quality of the consensus
qpc = sum(sum(abs(diff(S2))));

Now im confuse whether it is correct to get the consensus partition using the line below

# Get the community/consensus partition
communities_static= teneto.communitydetection.temporal_louvain(tnet_static, intersliceweight=0.1, n_iter=1)

or using the logic as in the consensus_iterative.

Sorry for out-topic question, but appreciate if you can share some insight to a beginner like myself