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Implement a New Graph

This is the developer tutorial for implementing a new graph. In this tutorial, you will learn how to create the generator file "*.gen.m" for a new graph, which can then be compiled by braph2genesis. All graphs are (direct or indirect) extensions of the base element Graph. Here, you will use as examples the graphs GraphBD (Binary Directed graph), MultilayerWU (Weighted Undirected multilayer graph), MultiplexBUT (Binary Undirected multiplex at fixed Thresholds), and OrdMxBUT (Binary Undirected ordinal multiplex with fixed Thresholds).

Implementation of unilayer graphs

Unilayer binary directed graph (GraphBD)

Implementation of multilayer graphs

Weighted directed multilayer graph (MultilayerWD)

Binary undirected multilayer graph with fixed thresholds (MultiplexBUT)

Binary undirected ordinal multiplex graph with fixed thresholds (OrdMxBUT)

Implementation of unilayer graphs ⬆

Unilayer binary directed graph (`GraphBD`) ⬆

You will start by implementing in detail GraphBD, which is a direct extension of Graph. A unilayer graph is constituted by nodes connected by edges, where the can be either 0 (absence of connection) or 1 (existence of connection).

Code 1. GraphBD element header. The header section of the generator code in "_GraphBD.gen.m" provides the general information about the GraphBD element.
%% ¡header!
GraphBD < Graph (g, binary directed graph) is a binary directed graph.  ①

%%% ¡description!  ②
In a binary directed (BD) graph, the edges are directed and they can be either 0 (absence of connection) or 1 (existence of connection).

%%% ¡build!  ③
1
① defines GraphBD as a subclass of Graph. The moniker will be g.

② provides a description of this graph.

③ defines the build number of the graph element.

Code 2. GraphBD element prop update. The props_update section of the generator code in "_GraphBD.gen.m" updates the properties of the Graph element. This defines the core properties of the graph.
%% ¡props_update!

%%% ¡prop!
NAME (constant, string) is the name of the binary directed graph.
%%%% ¡default!
'GraphBD'

%%% ¡prop!
DESCRIPTION (constant, string) is the description of the  binary directed graph.
%%%% ¡default!
'In a binary directed (BD) graph, the edges are directed and they can be either 0 (absence of connection) or 1 (existence of connection).'

%%% ¡prop!
TEMPLATE (parameter, item) is the template of the  binary directed graph.

%%% ¡prop!
ID (data, string) is a few-letter code of the  binary directed graph.
%%%% ¡default!
'GraphBD ID'

%%% ¡prop!
LABEL (metadata, string) is an extended label of the binary directed graph.
%%%% ¡default!
'GraphBD label'

%%% ¡prop!
NOTES (metadata, string) are some specific notes about the binary directed graph.
%%%% ¡default!
'GraphBD notes'

%%% ¡prop!  ①
GRAPH_TYPE (constant, scalar) returns the graph type __Graph.GRAPH__.
%%%% ¡default!
Graph.GRAPH

%%% ¡prop!  ②
CONNECTIVITY_TYPE (query, smatrix) returns the connectivity type __Graph.BINARY__.
%%%% ¡default!
value = Graph.BINARY;

%%% ¡prop!  ③
DIRECTIONALITY_TYPE  (query, smatrix) returns the directionality type __Graph.DIRECTED__.
%%%% ¡default! 
value = Graph.DIRECTED;

%%% ¡prop!  ④
SELFCONNECTIVITY_TYPE (query, smatrix) returns the self-connectivity type __Graph.NONSELFCONNECTED__.
%%%% ¡default!
value = Graph.NONSELFCONNECTED;

%%% ¡prop!  ⑤
NEGATIVITY_TYPE (query, smatrix) returns the negativity type __Graph.NONNEGATIVE__.
%%%% ¡default!
value = Graph.NONNEGATIVE;

%%% ¡prop!  ⑥
A (result, cell) is the binary adjacency matrix of the binary directed graph.
%%%% ¡calculate!
B = g.get('B');  ⑦

B = dediagonalize(B);   ⑧
B = semipositivize(B, 'SemipositivizeRule', g.get('SEMIPOSITIVIZE_RULE'));  ⑨
B = binarize(B);  ⑩

A = {B};  ⑪
if g.get('RANDOMIZE')  ⑫
    random_A = g.get('RANDOMIZATION', A);
    A = {random_A};
end
value = A;  ⑬
%%%% ¡gui!  ⑭
pr = PanelPropCell('EL', g, 'PROP', GraphBD.A, ... 
    'TABLE_HEIGHT', s(40), ... 
    'XSLIDERSHOW', false, ... 
    'YSLIDERSHOW', false, ...  
    'ROWNAME' , g.getCallback('ANODELABELS'), ... 
    'COLUMNNAME', g.getCallback('ANODELABELS'));

%%% ¡prop!  ⑮
COMPATIBLE_MEASURES (constant, classlist) is the list of compatible measures.
%%%% ¡default!
getCompatibleMeasures('GraphBD')
① defines the graph type: Graph.GRAPH (single layer), Graph.MULTIGRAPH (multiple unconnected layers), Graph.MULTILAYER (multiple layers), Graph.ORDERED_MULTILAYER (multiple subsequent layers) Graph.MULTIPLEX (multilayer with connections between corresponding nodes), and Graph.ORDERED_MULTIPLEX (multilayer with connections between corresponding nodes in subsequent layers).

② defines the graph connectivity: Graph.BINARY (0 or 1) or Graph.WEIGHTED.

③ defines the edge directionality: Graph.DIRECTED or Graph.UNDIRECTED.

④ defines the graph self-connectivity: Graph.NONSELFCONNECTED or Graph.SELFCONNECTED.

⑤ defines the graph negativity: Graph.NONNEGATIVE or Graph.NEGATIVE.

⑥ The property A contains the supra-adjacency matrix of the graph, which is calculated by the code under ¡calculate!.

⑦ retrieves the adjacency matrix of the graph B, defined in the new properties below.

⑧, ⑨, and ⑩ condition the adjaciency matrix removing the diagonal elements, making it semidefinte positive, and binarizing it. A list of useful functions is: diagonalize (removes the off-diagonal), dediagonalize (removes the diagonal), binarize (binarizes with threshold=0), semipositivize (removes negative weights), standardize (normalizes between 0 and 1) or symmetrize (symmetrizes the matrix). Use the MatLab help to see additional functionalities.

⑪ preallocates the adjacency matrix to be calculated.

⑫ randomizes adjacency matrix when 'RANDOMIZE' is true by calling the function of the graph named RANDOMIZATION

⑬ returns the calculated graph A assigning it to the output variable value.

⑭ employs the property panel PanelPropCell to be employed to visualize A, setting also its properties.

⑮ determines the list of compatible figures.

Code 3. GraphBD element props. The props section of the generator code in "_GraphBD.gen.m" defines the properties to be used in GraphBD.
%% ¡props!

%%% ¡prop! ①
B (data, smatrix) is the input graph adjacency matrix.
%%%% ¡gui!  ②
pr = PanelPropMatrix('EL', g, 'PROP', GraphBD.B, ... 
    'TABLE_HEIGHT' , s(40), ...
    'ROWNAME' , g.getCallback('ANODELABELS'), ... 
    'COLUMNNAME', g.getCallback('ANODELABELS'), ...
    varargin{:});

%%% ¡prop!  ③
SEMIPOSITIVIZE_RULE (parameter, option) determines how to remove the negative edges.
%%%% ¡settings!
{'zero', 'absolute'}

%%% ¡prop! ④
ATTEMPTSPEREDGE (parameter, scalar) is the attempts to rewire each edge.
%%%% ¡default!
5

%%% ¡prop! ⑤
RANDOMIZATION (query, cell) randomizes matrix contained in the cell.
%%%% ¡calculate!
rng(g.get('RANDOM_SEED'), 'twister')

if isempty(varargin)  ⑥
    value = {};
    return
end

A = cell2mat(varargin{1});
attempts_per_edge = g.get('ATTEMPTSPEREDGE');
% remove self connections
A(1:length(A)+1:numel(A)) = 0;
[I_edges, J_edges] = find(A);   ⑦
E = length(I_edges);  ⑧

if E == 0  ⑨
    value = A;
    swaps = 0;
    return
end

if E == 1  ⑩
    r_ab = A(I_edges(1), J_edges(1));
    A(I_edges(1), J_edges(1)) = 0;
    selected_nodes = randperm(size(A, 1), 2);
    A(selected_nodes(1), selected_nodes(2)) = r_ab;
    value = A;
    swaps = 1;
    return
end

random_A = A;
swaps = 0; % number of successful edge swaps
for attempt = 1:1:attempts_per_edge*E  ⑪

    selected_edges = randperm(E,2);  ⑫
    node_start_1 = I_edges(selected_edges(1));
    node_end_1 = J_edges(selected_edges(1));
    node_start_2 = I_edges(selected_edges(2));
    node_end_2 = J_edges(selected_edges(2));

    r_1 = random_A(node_start_1, node_end_1);  ⑬
    r_2 = random_A(node_start_2, node_end_2);

    if ~random_A(node_start_1, node_end_2) && ...
    ~random_A(node_start_2, node_end_1) && ...
    node_start_1~=node_start_2 && ...
    node_end_1~=node_end_2 && ...
    node_start_1~=node_end_2 && ...
    node_start_2~=node_end_1
    
        % erase old edges  ⑭
        random_A(node_start_1, node_end_1) = 0;
        random_A(node_start_2, node_end_2) = 0;

        % write new edges  ⑮
        random_A(node_start_1, node_end_2) = r_1;
        random_A(node_start_2, node_end_1) = r_2;
        
        % update edge list
        J_edges(selected_edges(1)) = node_end_2;
        J_edges(selected_edges(2)) = node_end_1;

        swaps = swaps+1;
    end
end
value = random_A;
① contains the input adjacency matrix B, which is typically weighted and directed.

② defines the property panel PanelPropMatrix to plot this property with a table.

③ defines the semi-positivation rule (i.e., how to remove the negative edges) to be used when generating the adjacency matrix A from the intput property B. The admissible options are: 'zero' (default, convert negative values to zeros) or 'absolute' (convert negative values to absolute value).

④ defines the number of attempts that will be used for each edge when calling RANDOMIZATION.

⑤ randomizes the adjacency matrix contained in cell.

⑥ returns empty cell is the input is an empty cell.

⑦ finds number of edges in the matrix (different from zero).

⑧ returns number of edges in the matrix (different from zero).

⑨ returns same input matrix if it is all zeros.

⑩ randomizes the edge when there is only one edge in the input matrix.

⑪ randomizes edges in the matrix when more than one edge (non-zero) were found in the input matrix.

⑫ takes two random edges.

⑬ saves the values of the selected random edges (this is important when the property RANDOMIZATION is used by weighted graphs).

⑭ deletes edges in the old positions.

⑮ sets values of edges in the new random positions.

Code 4. GraphBD element tests. The tests section in the element generator "_GraphBD.gen.m". A general test should be prepared to test the properties of the graph when it is empty and full. Furthermore, additional tests should be prepared for the defined rules (one test per rule).
%% ¡tests!

%%% ¡excluded_props!   ①
[GraphBD.PFGA GraphBD.PFGH]

%%% ¡test!
%%%% ¡name!
Constructor - Empty   ②
%%%% ¡probability!  ③
.01
%%%% ¡code!
B = [];  ④
g = GraphBD('B', B); ⑤

g.get('A_CHECK');  ⑥

A = {binarize(semipositivize(dediagonalize(B)))};  ⑦
assert(isequal(g.get('A'), A), ... ⑧
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD is not constructing well.')

%%% ¡test!
%%%% ¡name!
Constructor - Full  ⑨
%%%% ¡probability!
.01
%%%% ¡code!
B = randn(randi(10));  ⑩
g = GraphBD('B', B);

g.get('A_CHECK')

A = {binarize(semipositivize(dediagonalize(B)))};
assert(isequal(g.get('A'), A), ...
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD is not constructing well.')

%%% ¡test!
%%%% ¡name!
Semipositivize Rules  ⑪
%%%% ¡probability!
.01  ③
%%%% ¡code!
B = [  ⑫
    -2 -1 0 1 2
    -1 0 1 2 -2
    0 1 2 -2 -1
    1 2 -2 -1 0
    2 -2 -1 0 1
    ];

g0 = GraphBD('B', B);   ⑬
A0 = {[  ⑭
    0 0 0 1 1
    0 0 1 1 0
    0 1 0 0 0
    1 1 0 0 0
    1 0 0 0 0
    ]};
assert(isequal(g0.get('A'), A0), ... 
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD is not constructing well.')

g_zero = GraphBD('B', B, 'SEMIPOSITIVIZE_RULE', 'zero');  ⑮
A_zero = {[
    0 0 0 1 1
    0 0 1 1 0
    0 1 0 0 0
    1 1 0 0 0
    1 0 0 0 0
    ]};
assert(isequal(g_zero.get('A'), A_zero), ...
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD is not constructing well.')

g_absolute = GraphBD('B', B, 'SEMIPOSITIVIZE_RULE', 'absolute');  ⑯
A_absolute = {[
    0 1 0 1 1
    1 0 1 1 1
    0 1 0 1 1
    1 1 1 0 0
    1 1 1 0 0
    ]};
assert(isequal(g_absolute.get('A'), A_absolute), ...
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD is not constructing well.')
    
%%% ¡test!
%%%% ¡name!
Randomize Rules  ⑰
%%%% ¡probability!
.01
%%%% ¡code!
B = randn(10);

g = GraphBD('B', B);
g.set('RANDOMIZE', true);
g.set('ATTEMPTSPEREDGE', 4);

A = g.get('A');

assert(isequal(size(A{1}), size(B)), ...  ⑱
[BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
'GraphBD Randomize is not functioning well.')

g2 = GraphBD('B', B);
g2.set('RANDOMIZE', false);
g2.set('ATTEMPTSPEREDGE', 4);
A2 = g2.get('A');
random_A = g2.get('RANDOMIZATION', A2);

if all(A2{1}==0, "all") ⑲
    assert(isequal(A2{1}, random_A), ...
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD Randomize is not functioning well.')
elseif isequal((length(A2{1}).^2)- length(A2{1}), sum(A2{1}==1, "all")) ⑳
    assert(isequal(A2{1}, random_A), ...
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD Randomize is not functioning well.')
else  ㉑
    assert(~isequal(A2{1}, random_A), ...
    [BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
    'GraphBD Randomize is not functioning well.')
end

assert(isequal(numel(find(A2{1})), numel(find(random_A))), ...  ㉒
[BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
'GraphBD Randomize is not functioning well.')

deg_A = sum(A2{1}, 2);
deg_B = sum(random_A, 2);
[h, p, ks2stat] = kstest2(deg_A, deg_B);

assert(isequal(0, h), ... %  ㉓
[BRAPH2.STR ':GraphBD:' BRAPH2.FAIL_TEST], ...
'GraphBD Randomize is not functioning well.')
① List of properties that are excluded from testing.

② checks that an empty GraphBD graph is constructing well.

③ assigns a low test execution probability.

④ initializes an empty input adjacency matrix B.

⑤ constructs the GraphBD graph from the initialized B.

⑥ performs the corresponding checks for the format of the adjacency matrix A: GRAPH_TYPE, CONNECTIVITY_TYPE, DIRECTIONALITY_TYPE, SELFCONNECTIVITY_TYPE, and NEGATIVITY_TYPE.

⑦ calculates the value of the graph by applying the corresponding functions.

⑧ tests that the value of generated graph calculated by applying the functions coincides with the expected value.

⑨ checks that a full GraphBD graph is constructing well.

⑩ generates a random input adjacency matrix B.

⑪ checks the SEMIPOSITIVIZE_RULE on the GraphBD graph.

⑫ generates an input adjacency matrix with negative weights.

⑬ constructs the GraphBD graph from the initialized B with default RULE for SEMIPOSITIVIZE_RULE.

⑭ provides the expected value of A calculated by external means.

⑮ constructs the GraphBD graph from the initialized B with RULE = 'zero' for SEMIPOSITIVIZE_RULE.

⑯ constructs the GraphBD graph from the initialized B with RULE = 'absolute' for SEMIPOSITIVIZE_RULE.

⑰ tests that RANZOMIZATION works properly.

⑱ tests that RANZOMIZATION returns a matrix with same size.

⑲ tests that RANZOMIZATION returns a matrix of zeros when input matrix is all zeros.

⑳ tests that RANZOMIZATION returns a matrix of ones when input matrix is all ones (except diagonal).

㉑ tests that new random matrix is different from original one.

㉒ tests that new random matrix has the same number of nodes as the original one

㉓ tests that new random matrix has the same degree distribution as the original one

Implementation of multilayer graphs ⬆

Weighted directed multilayer graph (`MultilayerWD`) ⬆

You can now use GraphBD as the basis to implement the MultilayerWD graph. A multilayer graph allows connections between any nodes across the multiple layers, where all layers are interconnected following a categorical fashion.

Code 5. MultilayerWD element header. The header section of generator code in "_MultilayerWD.gen.m" provides the general information about the MultilayerWD element. This code modifies Code 1.

%% ¡header!
MultilayerWD < Graph (g, multilayer weighted directed graph) is a multilayer weighted directed graph.

%%% ¡description!
In a multilayer weighted directed (WD) graph, layers could have different number of nodes with within-layer weighted directed edges, associated with a real number between 0 and 1 and indicating the strength of the connection. The connectivity matrices are symmetric (within layer). All node connections are allowed between layers.

%%% ¡build!
1

Code 6. MultilayerWD element prop update. The props_update section of the generator code in "_MultilayerWD.gen.m" updates the properties of MultilayerWD. This code modifies Code 2.

%% ¡props_update!

%%% ¡prop!
NAME (constant, string) is the name of the multilayer weighted directed graph.
%%%% ¡default!
'MultilayerWD'

%%% ¡prop!
DESCRIPTION (constant, string) is the description of the multilayer weighted directed graph.
%%%% ¡default!
'In a multilayer weighted directed (WD) graph, layers could have different number of nodes with within-layer weighted directed edges, associated with a realnumber between 0 and 1 and indicating the strength of the connection. The connectivity matrices are symmetric (within layer). All node connections are allowed between layers.'

%%% ¡prop!
TEMPLATE (parameter, item) is the template of the multilayer weighted directed graph.

%%% ¡prop!
ID (data, string) is a few-letter code of the multilayer weighted directed graph.
%%%% ¡default!
'MultilayerWD ID'

%%% ¡prop!
LABEL (metadata, string) is an extended label of the multilayer weighted directed graph.
%%%% ¡default!
'MultilayerWD label'

%%% ¡prop!
NOTES (metadata, string) are some specific notes about the multilayer weighted directed graph.
%%%% ¡default!
'MultilayerWD notes'

%%% ¡prop!
GRAPH_TYPE (constant, scalar) returns the graph type __Graph.MULTILAYER__.
%%%% ¡default!
Graph.MULTILAYER

%%% ¡prop!
CONNECTIVITY_TYPE (query, smatrix) returns the connectivity type __Graph.WEIGHTED__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
layernumber = 1;
else
layernumber = varargin{1};
end
value = Graph.WEIGHTED * ones(layernumber);

%%% ¡prop!
DIRECTIONALITY_TYPE (query, smatrix) returns the directionality type __Graph.DIRECTED__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.DIRECTED * ones(layernumber);

%%% ¡prop!
SELFCONNECTIVITY_TYPE (query, smatrix) returns the self-connectivity type __Graph.NONSELFCONNECTED__ on the diagonal and __Graph.SELFCONNECTED__ off diagonal.
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.SELFCONNECTED * ones(layernumber);
value(1:layernumber+1:end) = Graph.NONSELFCONNECTED;                

%%% ¡prop!
NEGATIVITY_TYPE (query, smatrix) returns the negativity type __Graph.NONNEGATIVE__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.NONNEGATIVE * ones(layernumber);

%%% ¡prop!
A (result, cell) is the cell containing the within-layer weighted adjacency
matrices of the multilayer weighted directed graph and the connections
between layers.

%%%% ¡calculate!
B = g.get('B'); 
L = length(B); 
A = cell(L, L);
for i = 1:1:L  ①
    M = dediagonalize(B{i,i}); 
    M = semipositivize(M, 'SemipositivizeRule', g.get('SEMIPOSITIVIZE_RULE'));
    M = standardize(M, 'StandardizeRule', g.get('STANDARDIZE_RULE'));  
    A(i, i) = {M};
    if ~isempty(A{i, i})
        for j = i+1:1:L
            M = semipositivize(B{i,j}, 'SemipositivizeRule',     g.get('SEMIPOSITIVIZE_RULE')); 
            M = standardize(M, 'StandardizeRule',     g.get('STANDARDIZE_RULE'));  
            A(i, j) = {M};
            M = semipositivize(B{j,i}, 'SemipositivizeRule',     g.get('SEMIPOSITIVIZE_RULE')); 
            M = standardize(M, 'StandardizeRule',     g.get('STANDARDIZE_RULE'));  
            A(j, i) = {M};
        end
    end
end
if g.get('RANDOMIZE')
    A = g.get('RANDOMIZATION', A);
end
value = A;
%%%% ¡gui!
pr = PanelPropCell('EL', g, 'PROP', MultilayerWD.A, ...
    'TABLE_HEIGHT', s(40), ...
    'XYSLIDERLOCK', true, ... 
    'XSLIDERSHOW', false, ...
    'YSLIDERSHOW', true, ...
    'YSLIDERLABELS', g.getCallback('ALAYERLABELS'), ...
    'YSLIDERWIDTH', s(5), ...
    'ROWNAME', g.getCallback('ANODELABELS'), ...
    'COLUMNNAME', g.getCallback('ANODELABELS'), ...
    varargin{:});

%%% ¡prop!
PARTITIONS (result, rvector) returns the number of layers in the partitions of the graph.
%%%% ¡calculate!
value = ones(1, g.get('LAYERNUMBER'));

%%% ¡prop!  ②
ALAYERLABELS (query, stringlist) returns the layer labels to be used by the slider.
%%%% ¡calculate!
alayerlabels = g.get('LAYERLABELS');  ③
if isempty(alayerlabels) && ~isa(g.getr('A'), 'NoValue') % ensures that it's not unecessarily calculated
    alayerlabels = cellfun(@num2str, num2cell([1:1:g.get('LAYERNUMBER')]), 'uniformoutput', false);  ④
end
value = alayerlabels;

%%% ¡prop!
COMPATIBLE_MEASURES (constant, classlist) is the list of compatible measures.
%%%% ¡default!
getCompatibleMeasures('MultilayerWD')

① For each layer in MultilayerWD graph, the corresponding functions are applied as in the notes ⑧, ⑨, and ⑩ of Code 2.

② These are some properties of the graph adjacency matrix A used in its visualization. The list of properties that can be used are: ALAYERTICKS (to set ticks for each layer according to the layer number), ALAYERLABELS (to set labels for each layer), and ANODELABELS (to set the nodal labels for each layer)).

③ returns the labels of the graph layers provided by the user.

④ constructs the labels of the layers based on the number of the layer (in case no layer labels were provided by the user).

Code 7. MultilayerWD element props. The props section of the generator code for "_MultilayerWD.gen.m" defines the properties to be used in MultilayerWD. This code modifies Code 3.

%% ¡props!

%%% ¡prop!
B (data, cell) is the input cell containing the multilayer adjacency matrices.
%%%% ¡default!
{[] []; [] []}
%%%% ¡gui!  ①
pr = PanelPropCell('EL', g, 'PROP', MultilayerWD.B, ...
    'TABLE_HEIGHT', s(40), ...
    'XSLIDERSHOW', true, ...
    'XSLIDERLABELS', g.get('LAYERLABELS'), ...
    'XSLIDERHEIGHT', s(3.5), ...
    'YSLIDERSHOW', false, ...
    'ROWNAME', g.getCallback('ANODELABELS'), ...
    'COLUMNNAME', g.getCallback('ANODELABELS'), ...
    varargin{:});


%%% ¡prop!
SEMIPOSITIVIZE_RULE (parameter, option) determines how to remove the negative edges.
%%%% ¡settings!
{'zero', 'absolute'}

%%% ¡prop!   ②
STANDARDIZE_RULE (parameter, option) determines how to normalize the weights between 0 and 1.
%%%% ¡settings!
{'threshold' 'range'}

%%% ¡prop!
ATTEMPTSPEREDGE (parameter, scalar) is the attempts to rewire each edge.
%%%% ¡default!
5

%%% ¡prop!
NUMBEROFWEIGHTS (parameter, scalar) specifies the number of weights sorted at the same time.   ③
%%%% ¡default!
10

%%% ¡prop!
RANDOMIZATION (query, cell) is the attempts to rewire each edge.
%%%% ¡calculate!
rng(g.get('RANDOM_SEED'), 'twister')

if isempty(varargin)
    value = {};
    return
end

A = varargin{1};
attempts_per_edge = g.get('ATTEMPTSPEREDGE');

for i = 1:length(A)  ④
    tmp_a = A{i,i};

    tmp_g = GraphWD();  ⑤
    tmp_g.set('ATTEMPTSPEREDGE', g.get('ATTEMPTSPEREDGE'));
    tmp_g.set('NUMBEROFWEIGHTS', g.get('NUMBEROFWEIGHTS'));
    random_A = tmp_g.get('RANDOMIZATION', {tmp_a});
    A{i, i} = random_A;
end
value = A;

① Same as in note ② of Code 3.

② Same as in note ③ of Code 3.

③ defines the number of weights that will be sorted at the same time when using RANDOMIZATION.

④ iterates over each layer in MultilayerWD to randomize it.

⑤ initizalizes empty GraphWD to get RANDOMIZATION property from it.

Code 8. MultilayerWD element tests. The tests section from the element generator "_MultilayerWD.gen.m". This code modifies Code 4.

%% ¡tests!

%%% ¡excluded_props!
[MultilayerWD.PFGA MultilayerWD.PFGH]

%%% ¡test!
%%%% ¡name!
Constructor - Full
%%%% ¡probability!
.01
%%%% ¡code!
B1 = rand(randi(10));
B2 = rand(randi(10));
B3 = rand(randi(10));
B12 = rand(size(B1, 1),size(B2, 2));
B13 = rand(size(B1, 1),size(B3, 2));
B23 = rand(size(B2, 1),size(B3, 2));
B21 = rand(size(B2, 1),size(B1, 2));
B31 = rand(size(B3, 1),size(B1, 2));
B32 = rand(size(B3, 1),size(B2, 2));
B = {
    B1                           B12                            B13
    B21                          B2                             B23
    B31                          B32                            B3
};
g = MultilayerWD('B', B);
g.get('A_CHECK')
A1 = standardize(semipositivize(dediagonalize(B1)));
A2 = standardize(semipositivize(dediagonalize(B2)));
A3 = standardize(semipositivize(dediagonalize(B3)));
A12 = standardize(semipositivize(B12));
A13 = standardize(semipositivize(B13));
A23 = standardize(semipositivize(B23));
A21 = standardize(semipositivize(B21));
A31 = standardize(semipositivize(B31));
A32 = standardize(semipositivize(B32));
B{1,1} = A1;
B{2,2} = A2;
B{3,3} = A3;
B{1,2} = A12;
B{1,3} = A13;
B{2,3} = A23;
B{2,1} = A21;
B{3,1} = A31;
B{3,2} = A32;
A = B;
assert(isequal(g.get('A'), A), ...
    [BRAPH2.STR ': MultilayerWD: ' BRAPH2.FAIL_TEST], ...
    'MultilayerWD  is not constructing well.')
    
%%% ¡test!
%%%% ¡name!
Randomize Rules
%%%% ¡probability!
.01
%%%% ¡code!
B1 = rand(randi(10));
B2 = rand(randi(10));
B3 = rand(randi(10));
B12 = rand(size(B1, 1),size(B2, 2));
B13 = rand(size(B1, 1),size(B3, 2));
B23 = rand(size(B2, 1),size(B3, 2));
B21 = rand(size(B2, 1),size(B1, 2));
B31 = rand(size(B3, 1),size(B1, 2));
B32 = rand(size(B3, 1),size(B2, 2));
B = {
    B1                           B12                            B13
    B21                          B2                             B23
    B31                          B32                            B3
};
g = MultilayerWD('B', B);
g.set('RANDOMIZE', true);
g.set('ATTEMPTSPEREDGE', 4);
g.get('A_CHECK')

A = g.get('A')

assert(isequal(size(A{1}), size(B{1})), ...
[BRAPH2.STR 'MultilayerWD:' BRAPH2.FAIL_TEST], ... 'MultilayerWD Randomize is not functioning well.')

g2 = MultilayerWD('B', B);
g2.set('RANDOMIZE', true);
g2.set('ATTEMPTSPEREDGE', 4);
g2.get('A_CHECK')
A2 = g2.get('A');
random_A = g2.get('RANDOMIZATION', A2);

for i = 1:length(A2)  ①
    if all(A2{i, i}==0, "all") %if all edges are zero, the new random matrix is all zeros
        assert(isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':MultilayerWD:' BRAPH2.FAIL_TEST], ...
        'MultilayerWD Randomize is not functioning well.')
    elseif isequal((length(A2{i, i}).^2)- length(A2{i, i}), sum(A2{i, i}==1, "all")) %if all nodes (except diagonal) are one, the random matrix is the same as original
        assert(isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':MultilayerWD:' BRAPH2.FAIL_TEST], ...
        'MultilayerWD Randomize is not functioning well.')
    else
        assert(~isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':MultilayerWD:' BRAPH2.FAIL_TEST], ...
        'MultilayerWD Randomize is not functioning well.')
    end
assert(isequal(numel(find(A2{i, i})), numel(find(random_A{i, i}))), ... % check same number of nodes
[BRAPH2.STR ':MultilayerWD:' BRAPH2.FAIL_TEST], ...
'MultilayerWD Randomize is not functioning well.')
end

① tests RANDOMIZATION as in Code 4 for each layer in A2.

Binary undirected multilayer graph with fixed thresholds (`MultiplexBUT`) ⬆

Now you will implement the MultiplexBUT graph building on the previous codes GraphBD and MultilayerWD. A multiplex graph is a type of multilayer graph where interlayer edges are allowed only between homologous nodes. In this case, the layers follow a categorical architecture, which means that all layers are interconnected.

Code 9. MultiplexBUT element header. The header section of the generator code in "_MultiplexBUT.gen.m" provides the general information about the MultiplexBUT element. This code modifies Code 1.
%% ¡header!
MultiplexBUT < MultiplexWU (g, binary undirected multiplex with fixed thresholds) is a binary undirected multiplex with fixed thresholds.  ①
    
%%% ¡description!
In a binary undirected multiplex with fixed thresholds (BUT), the layers are those of binary undirected (BU) multiplex graphs derived from the same weighted supra-connectivity matrices binarized at different thresholds.The supra-connectivity matrix has a number of partitions equal to the number of thresholds.

%%% ¡build!
1
① MultiplexBUT is a child of MultiplexWU, which in turn derives from Graph.

Code 10. MultiplexBUT element prop update. The props_update section of the generator code in "_MultiplexBUT.gen.m" updates the properties of MultiplexBUT. This code modifies Code 2.

%% ¡props_update!

%%% ¡prop!
NAME (constant, string) is the name of the binary undirected multiplex with fixed thresholds.
%%%% ¡default!
'MultiplexBUT'

%%% ¡prop!
DESCRIPTION (constant, string) is the description of the binary undirected multiplex with fixed thresholds.
%%%% ¡default!
'In a binary undirected multiplex with fixed thresholds (BUT), the layers are those of binary undirected (BU) multiplex graphs derived from the same weighted supra-connectivity matrices binarized at different thresholds. The supra-connectivity matrix has a number of partitions equal to the number of thresholds.'

%%% ¡prop!
TEMPLATE (parameter, item) is the template of the binary undirected multiplex with fixed thresholds.

%%% ¡prop!
ID (data, string) is a few-letter code of the binary undirected multiplex with fixed thresholds.
%%%% ¡default!
'MultiplexBUT ID'

%%% ¡prop!
LABEL (metadata, string) is an extended label of the binary undirected multiplex with fixed thresholds.
%%%% ¡default!
'MultiplexBUT label'

%%% ¡prop!
NOTES (metadata, string) are some specific notes about the binary undirected multiplex with fixed thresholds.
%%%% ¡default!
'MultiplexBUT notes'
    
%%% ¡prop!
GRAPH_TYPE (constant, scalar) returns the graph type __Graph.MULTIPLEX__.
%%%% ¡default!
Graph.MULTIPLEX
    
%%% ¡prop!
CONNECTIVITY_TYPE (query, smatrix) returns the connectivity type __Graph.BINARY__  * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.BINARY * ones(layernumber); 

%%% ¡prop!
DIRECTIONALITY_TYPE (query, smatrix) returns the directionality type __Graph.UNDIRECTED__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.UNDIRECTED * ones(layernumber);
    
%%% ¡prop!
SELFCONNECTIVITY_TYPE (query, smatrix) returns the self-connectivity type __Graph.NONSELFCONNECTED__ on the diagonal and __Graph.SELFCONNECTED__ off diagonal.
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.SELFCONNECTED * ones(layernumber);
value(1:layernumber+1:end) = Graph.NONSELFCONNECTED;                
    
%%% ¡prop!
NEGATIVITY_TYPE (query, smatrix) returns the negativity type __Graph.NONNEGATIVE__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.NONNEGATIVE * ones(layernumber);. . . . .%%% ¡prop!
A (result, cell) is the cell containing multiplex binary adjacency matrices of the binary undirected multiplex.
    
%%%% ¡calculate!
A_WU = calculateValue@MultiplexWU(g, prop); ①
    
thresholds = g.get('THRESHOLDS');  ②
L = length(A_WU); % number of layers  ③
A = cell(length(thresholds) * L);  ④
    
if L > 0 && ~isempty(cell2mat(A_WU))
    A(:, :) = {eye(length(A_WU{1, 1}))};
    for i = 1:1:length(thresholds)  ⑤
        threshold = thresholds(i);
        layer = 1;
        for j = (i - 1) * L + 1:1:i * L  ⑥
            A{j, j} = dediagonalize(binarize(A_WU{layer, layer}, 'threshold', threshold));  ⑦
            layer = layer + 1;
        end
    end
end
if g.get('RANDOMIZE')
    A = g.get('RANDOMIZATION', A);
end
value = A;

%%%% ¡gui!  ⑧
pr = PanelPropCell('EL', g, 'PROP', MultiplexBUT.A, ...
    'TABLE_HEIGHT', s(40), ...
    'XYSLIDERLOCK', true, ... 
    'XSLIDERSHOW', false, ...
    'YSLIDERSHOW', true, ...
    'YSLIDERLABELS', g.getCallback('ALAYERLABELS'), ...
    'YSLIDERWIDTH', s(5), ...
    'ROWNAME', g.getCallback('ANODELABELS'), ...
    'COLUMNNAME', g.getCallback('ANODELABELS'), ...
    varargin{:});. . . . .%%% ¡prop!
PARTITIONS (result, rvector) returns the number of layers in the partitions of the graph.
%%%% ¡calculate!
l = g.get('LAYERNUMBER');
thresholds = g.get('THRESHOLDS');
value = ones(1, length(thresholds)) * l / length(thresholds);
    
%%% ¡prop!
ALAYERLABELS (query, stringlist) returns the layer labels to be used by the slider.
%%%% ¡calculate!
alayerlabels = g.get('LAYERLABELS');
if ~isa(g.getr('A'), 'NoValue') && length(alayerlabels) ~= g.get('LAYERNUMBER') % ensures that it's not unecessarily calculated
    thresholds = cellfun(@num2str, num2cell(g.get('THRESHOLDS')), 'uniformoutput', false);

    if length(alayerlabels) == length(g.get('B'))
        blayerlabels = alayerlabels;
    else % includes isempty(layerlabels)
        blayerlabels = cellfun(@num2str, num2cell([1:1:length(g.get('B'))]), 'uniformoutput', false);
    end
    
    alayerlabels = {};
    for i = 1:1:length(thresholds) ⑨
        for j = 1:1:length(blayerlabels)
            alayerlabels = [alayerlabels, [blayerlabels{j} '|' thresholds{i}]];
        end
    end
end
value = alayerlabels;

%%% ¡prop! 
COMPATIBLE_MEASURES (constant, classlist) is the list of compatible measures.
%%%% ¡default!
getCompatibleMeasures('MultiplexBUT')

%%% ¡prop!
ATTEMPTSPEREDGE (parameter, scalar) is the attempts to rewire each edge.
%%%% ¡default!
5

%%% ¡prop!
RANDOMIZATION (query, cell) is the attempts to rewire each edge.
%%%% ¡calculate!
rng(g.get('RANDOM_SEED'), 'twister')

if isempty(varargin)
    value = {};
    return
end

A = varargin{1};
attempts_per_edge = g.get('ATTEMPTSPEREDGE');

for i = 1:length(A)
    tmp_a = A{i,i};

    random_g = GraphBU();   ⑩
    random_g.set('ATTEMPTSPEREDGE', g.get('ATTEMPTSPEREDGE'));
    random_A = random_g.get('RANDOMIZATION', {tmp_a});
    A{i, i} = random_A;
end
value = A;

① calculates the graph MultiplexWU calling its parent MultiplexWU.

② gets the thresholds to be applied to A_WU.

③ gets the number of layers in graph A_WU.

④ The new MultiplexBUT graph will have L layers for each threshold applied.

⑤ iterates over all the thresholds to be applied.

⑥ iterates over all the layers in A_WU.

⑦ binarizes the present layer of the A_WU graph according to the present threshold.

⑧ Same as in note ② of Code 2.

⑨ sets the labels of the layers considering the thresholds and the number of layers in each multiplex graph for each threshold

⑩ Same as in Code 6 but using GraphBU.

Code 11. MultiplexBUT element props. The props section of the generator code in "_MultiplexBUT.gen.m" defines the properties to be used in MultiplexBUT. This code modifies Code 3.
%% ¡props!
    
%%% ¡prop!
THRESHOLDS (parameter, rvector) is the vector of thresholds.
%%%% ¡gui!  ①
pr = PanelPropRVectorSmart('EL', g, 'PROP', MultiplexBUT.THRESHOLDS, ...
    'MAX', 1, ...
    'MIN', -1, ...
    varargin{:});
① PanelPropRVectorSmart plots the panel for a row vector with an edit field. Smart means that (almost) any MatLab expression leading to a correct row vector can be introduced in the edit field. Also, the value of the vector can be limited between some MIN and MAX.

Code 12. MultiplexBUT element tests. The tests section from the element generator "_MultiplexBUT.gen.m". This code modifies Code 4.

%% ¡tests!

%%% ¡test!
%%%% ¡name!
Constructor - Full
%%%% ¡probability!
.01
%%%% ¡code!
B1 = [
    0 .1 .2 .3 .4 
    .1 0 .1 .2 .3
    .2 .1 0 .1 .2
    .3 .2 .1 0 .1
    .4 .3 .2 .1 0
    ]; 
B = {B1, B1, B1};  ①
thresholds = [0 .1 .2 .3 .4];  ②
g = MultiplexBUT('B', B, 'THRESHOLDS', thresholds);
    
g.get('A_CHECK')
    
A = g.get('A');
for i = 1:1:length(B) * length(thresholds)
    for j = 1:1:length(B) * length(thresholds)
        if i == j
            threshold = thresholds(floor((i - 1) / length(B)) + 1);
            assert(isequal(A{i, i}, binarize(B1, 'threshold', threshold)), ...
            [BRAPH2.STR ':MultiplexBUT:' BRAPH2.FAIL_TEST], ...
            'MultiplexBUT is not constructing well.')
        else
            assert(isequal(A{i, j}, eye(length(B1))), ...
            [BRAPH2.STR ':MultiplexBUT:' BRAPH2.FAIL_TEST], ...
            'MultiplexBUT is not constructing well.')            
        end
    end
end

%%% ¡test!
%%%% ¡name!
Randomize Rules
%%%% ¡probability!
.01
%%%% ¡code!
B11 = randn(10);

B12 = rand(size(B11,1),size(B11,2));

B= {B11 B12 B12;
    B12 B11 B12;
    B12 B12 B11};
thresholds = [0 .5 1];
g = MultilayerBUT('B', B, 'THRESHOLDS', thresholds); 

g.set('RANDOMIZE', true);
g.set('ATTEMPTSPEREDGE', 4);
g.get('A_CHECK')

A = g.get('A');

assert(isequal(size(A{1}), size(B{1})), ...
[BRAPH2.STR  ':MultilayerBUT:'  BRAPH2.FAIL_TEST], ...  'MultilayerBUT Randomize is not functioning well.')

g2 = MultilayerBUT('B', B, 'THRESHOLDS', thresholds); 
g2.set('RANDOMIZE', false);
g2.set('ATTEMPTSPEREDGE', 4);
A2 = g2.get('A');
random_A = g2.get('RANDOMIZATION', A2);

for i = 1:length(A2)
     if all(A2{i, i}==0, "all") %if all edges are zero, the new random matrix is all zeros
        assert(isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':MultilayerBUT:' BRAPH2.FAIL_TEST], ...
        'MultilayerBUT Randomize is not functioning well.')
    elseif isequal((length(A2{i, i}).^2)- length(A2{i, i}), sum(A2{i, i}==1, "all")) %if all nodes (except diagonal) are one, the random matrix is the same as original
        assert(isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':MultilayerBUT:' BRAPH2.FAIL_TEST], ...
        'MultilayerBUT Randomize is not functioning well.')
    else
        assert(~isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':MultilayerBUT:' BRAPH2.FAIL_TEST], ...
        'MultilayerBUT Randomize is not functioning well.')
    end

assert(isequal(numel(find(A2{i, i})), numel(find(random_A{i, i}))), ... % check same number of nodes
[BRAPH2.STR ':MultilayerBUT:' BRAPH2.FAIL_TEST], ...
'MultilayerBUT Randomize is not functioning well.')

assert(issymmetric(random_A{i, i}), ... % check symmetry  ③
[BRAPH2.STR ':MultilayerBUT:' BRAPH2.FAIL_TEST], ...
'MultilayerBUT Randomize is not functioning well.')

end

① creates an example of the necessary input adjacency matrices.

② defines the thresholds.

③ checks symmetry of each layer in the new random graph random_A since they are undirected.

Binary undirected ordinal multiplex graph with fixed thresholds (`OrdMxBUT`) ⬆

Finally, you will implement the OrdMxBUT graph based on the previous codes GraphBD, MultilayerWD and MultiplexBUT.An ordered multiplex is a type of multiplex graph that consists of a sequence of layers with edges between corresponding nodes in subsequent layers.

Code 13. OrdMxBUT element header. The header section of the generator code in "_OrdMxBUT.gen.m" provides the general information about the OrdMxBUT element. This code modifies Code 1.

%% ¡header!
OrdMxBUT < OrdMxWU (g, ordinal multiplex binary undirected with fixed thresholds) is a binary undirected ordinal multiplex with fixed thresholds.  ①
    
%%% ¡description!
In a binary undirected ordinal multiplex with fixed thresholds (BUT), all the layers consist of binary undirected (BU) multiplex graphs derived from the same weighted supra-connectivity matrices binarized at different thresholds. The supra-connectivity matrix has a number of partitions equal to the number of thresholds. The layers are connected in an ordinal fashion, i.e., only consecutive layers are connected.

%%% ¡build!
1

① OrdMxBUT is a child of OrdMxWU, which in turn derives from Graph.

Code 14. OrdMxBUT element prop update. The props_update section of the generator code in "_OrdMxBUT.gen.m" updates the properties of OrdMxBUT. This code modifies Code 10.

%% ¡props_update!

%%% ¡prop!
NAME (constant, string) is the name of the binary undirected ordinal multiplex with fixed thresholds.s.
%%%% ¡default!
'OrdMxBUT'
    
%%% ¡prop!
DESCRIPTION (constant, string) is the description of the binary undirected ordinal multiplex with fixed thresholds..
%%%% ¡default!
'In a binary undirected ordinal multiplex with fixed thresholds (BUT), all the layers consist of binary undirected (BU) multiplex graphs derived from the same weighted supra-connectivity matrices binarized at different thresholds. The supra-connectivity matrix has a number of partitions equal to the number of thresholds. The layers are connectedin an ordinal fashion, i.e., only consecutive layers are connected.'
    
%%% ¡prop!
TEMPLATE (parameter, item) is the template of the binary undirected ordinal multiplex with fixed thresholds.. . . . .%%% ¡prop!
ID (data, string) is a few-letter code of the binary undirected ordinal multiplex with fixed thresholds.
%%%% ¡default!
'OrdMxBUT ID'

%%% ¡prop!
LABEL (metadata, string) is an extended label of the binary undirected ordinal multiplex with fixed thresholds.
%%%% ¡default!
'OrdMxBUT label'

%%% ¡prop!
NOTES (metadata, string) are some specific notes about the binary undirected ordinal multiplex with fixed thresholds.
%%%% ¡default!
'OrdMxBUT notes'

%%% ¡prop!
GRAPH_TYPE (constant, scalar) returns the graph type __Graph.ORDERED_MULTIPLEX__.
%%%% ¡default!
Graph.ORDERED_MULTIPLEX

%%% ¡prop!
CONNECTIVITY_TYPE (query, smatrix) returns the connectivity type __Graph.BINARY__  * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.BINARY * ones(layernumber); . . . . .%%% ¡prop!
DIRECTIONALITY_TYPE (query, smatrix) returns the directionality type __Graph.UNDIRECTED__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.UNDIRECTED * ones(layernumber);. . . . .%%% ¡prop!
SELFCONNECTIVITY_TYPE (query, smatrix) returns the self-connectivity type __Graph.NONSELFCONNECTED__ on the diagonal and __Graph.SELFCONNECTED__ off diagonal.
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.SELFCONNECTED * ones(layernumber);
value(1:layernumber+1:end) = Graph.NONSELFCONNECTED;                
    
%%% ¡prop!
NEGATIVITY_TYPE (query, smatrix) returns the negativity type __Graph.NONNEGATIVE__ * ones(layernumber).
%%%% ¡calculate!
if isempty(varargin)
    layernumber = 1;
else
    layernumber = varargin{1};
end
value = Graph.NONNEGATIVE * ones(layernumber);. . . . .%%% ¡prop!
A (result, cell) is the cell containingbinary supra-adjacency matrix of the binary undirected multiplex with fixed thresholds (BUT).
    
%%%% ¡calculate!
A_WU = calculateValue@OrdMxWU(g, prop); ①
    
thresholds = g.get('THRESHOLDS');   ②
L = length(A_WU); % number of layers 
A = cell(length(thresholds)*L);
    
if L > 0 && ~isempty(cell2mat(A_WU))
    A(:, :) = {zeros(length(A_WU{1, 1}))};
    for i = 1:1:length(thresholds)  ③
        threshold = thresholds(i);
        layer = 1;
        for j = (i - 1) * L + 1:1:i * L  ④
            for k = (i - 1) * L + 1:1:i * L
                if j == k  ⑤
                    A{j, j} = dediagonalize(binarize(A_WU{layer, layer}, 'threshold', threshold));
                elseif (j-k)==1 || (k-j)==1  ⑥
                    A(j, k) = {eye(length(A{1, 1}))};
                else  ⑦
                    A(j, k) = {zeros(length(A{1, 1}))};
                end
            end
            layer = layer + 1;
        end
    end
end
if g.get('RANDOMIZE')
    A = g.get('RANDOMIZATION', A);
end
value = A;. . . . .%%%% ¡gui!
pr = PanelPropCell('EL', g, 'PROP', OrdMxBUT.A, ...
    'TABLE_HEIGHT', s(40), ...
    'XYSLIDERLOCK', true, ... 
    'XSLIDERSHOW', false, ...
    'YSLIDERSHOW', true, ...
    'YSLIDERLABELS', g.getCallback('ALAYERLABELS'), ...
    'YSLIDERWIDTH', s(5), ...
    'ROWNAME', g.getCallback('ANODELABELS'), ...
    'COLUMNNAME', g.getCallback('ANODELABELS'), ...
    varargin{:});. . . . .%%% ¡prop!
PARTITIONS (result, rvector) returns the number of layers in the partitions of the graph.
%%%% ¡calculate!
l = g.get('LAYERNUMBER');
thresholds = g.get('THRESHOLDS');
value = ones(1, length(thresholds)) * l / length(thresholds);. . . . .%%% ¡prop!
ALAYERLABELS (query, stringlist) returns the layer labels to be used by the slider.
%%%% ¡calculate!
alayerlabels = g.get('LAYERLABELS');
if ~isa(g.getr('A'), 'NoValue') && length(alayerlabels) ~= g.get('LAYERNUMBER') % ensures that it's not unecessarily calculated
    thresholds = cellfun(@num2str, num2cell(g.get('THRESHOLDS')), 'uniformoutput', false);

    if length(alayerlabels) == length(g.get('B'))
        blayerlabels = alayerlabels;
    else % includes isempty(layerlabels)
        blayerlabels = cellfun(@num2str, num2cell([1:1:length(g.get('B'))]), 'uniformoutput', false);
    end
        
    alayerlabels = {};
    for i = 1:1:length(thresholds)
        for j = 1:1:length(blayerlabels)
            alayerlabels = [alayerlabels, [blayerlabels{j} '|' thresholds{i}]];
        end
    end
end
value = alayerlabels;. . . . .%%% ¡prop!
COMPATIBLE_MEASURES (constant, classlist) is the list of compatible measures.
%%%% ¡default!
getCompatibleMeasures('OrdMxBUT')

%%% ¡prop!
ATTEMPTSPEREDGE (parameter, scalar) is the attempts to rewire each edge.
%%%% ¡default!
5

%%% ¡prop!
RANDOMIZATION (query, cell) is the attempts to rewire each edge.  ⑧
%%%% ¡calculate!
rng(g.get('RANDOM_SEED'), 'twister')

if isempty(varargin)
    value = {};
    return
end

A = varargin{1};
attempts_per_edge = g.get('ATTEMPTSPEREDGE');

for i = 1:length(A)
    tmp_a = A{i,i};

    random_g = GraphBU();
    random_g.set('ATTEMPTSPEREDGE', g.get('ATTEMPTSPEREDGE'));
    random_A = random_g.get('RANDOMIZATION', {tmp_a});
    A{i, i} = random_A;
end
value = A;

① calculates the graph OrdMxWU calling the parent OrdMxWU.

② Same as in notes ②, ③, and ④ of Code 10..

③ constructs an ordinal muliplex binary undirected graph for each threshold.

④ loops over the layers of A_Wu for each threshold.

⑤ sets the layers constructed by binarizing A_Wu according to the present threshold on the diagonal of the supra-adjacency matrix.

⑥ connects consecutive layers.

⑦ does NOT connect NON-consecutive layers.

⑧ same as in Code 10.

Code 15. OrdMxBUT element props. The props section of generator code for "_OrdMxBUT.gen.m" defines the properties to be used in MultiplexBUT. This code modifies Code 11.
%% ¡props!

%%% ¡prop!
THRESHOLDS (parameter, rvector) is the vector of thresholds.
%%%% ¡gui!
pr = PanelPropRVectorSmart('EL', g, 'PROP', OrdMxBUT.THRESHOLDS,  ...
    'MAX', 1, ...
    'MIN', -1, ...
    varargin{:});

Code 16. OrdMxBUT element tests. The tests section from the element generator "_OrdMxBUT.gen.m". This code modifies Code 12.

%% ¡tests!

%%% ¡excluded_props!
[OrdMxBUT.PFGA OrdMxBUT.PFGH]

%%% ¡test!
%%%% ¡name!
Constructor - Full
%%%% ¡probability!
.01
%%%% ¡code!
B1 = [
    0 .1 .2 .3 .4 
    .1 0 .1 .2 .3
    .2 .1 0 .1 .2
    .3 .2 .1 0 .1
    .4 .3 .2 .1 0
    ];
B = {B1, B1, B1};
thresholds = [0 .1 .2 .3 .4];
g = OrdMxBUT('B', B, 'THRESHOLDS', thresholds);
    
g.get('A_CHECK')
    
A = g.get('A');
for i = 1:1:length(thresholds)
    threshold = thresholds(i);
    for j = (i - 1) * length(B) + 1:1:i * length(B)
        for k = (i - 1) * length(B) + 1:1:i * length(B)
            if j == k
                assert(isequal(A{j, j}, binarize(B1, 'threshold', threshold)), ...
                    [BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
                    'OrdMxBUT is not constructing well.')
            elseif (j-k)==1 || (k-j)==1
                assert(isequal(A{j, k}, eye(length(B1))), ...
                    [BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
                    'OrdMxBUT is not constructing well.')
            else 
                assert(isequal(A{j, k}, zeros(length(B1))), ...
                    [BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
                    'OrdMxBUT is not constructing well.')
            end
        end
    end
end

%%% ¡test!
%%%% ¡name!
Randomize Rules   ①
%%%% ¡probability!
.01
%%%% ¡code!
B1 = randn(10);
B = {B1, B1, B1};
thresholds = [0 .1 .2 .3 .4];
g = OrdMxBUT('B', B, 'THRESHOLDS', thresholds);

g.set('RANDOMIZE', true);
g.set('ATTEMPTSPEREDGE', 4);
g.get('A_CHECK')

A = g.get('A');

assert(isequal(size(A{1}), size(B{1})), ...
[BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
'OrdMxBUT Randomize is not functioning well.')

g2 = OrdMxBUT('B', B, 'THRESHOLDS', thresholds);
g2.set('RANDOMIZE', false);
g2.set('ATTEMPTSPEREDGE', 4);
A2 = g2.get('A');
random_A = g2.get('RANDOMIZATION', A2);

for i = 1:length(A2)
    if all(A2{i, i}==0, "all") %if all edges are zero, the new random matrix is all zeros
        assert(isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
        'OrdMxBUT Randomize is not functioning well.')
        elseif isequal((length(A2{i, i}).^2)- length(A2{i, i}), sum(A2{i, i}==1, "all")) %if all nodes (except diagonal) are one, the random matrix is the same as original
        assert(isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
        'OrdMxBUT Randomize is not functioning well.')
    else
        assert(~isequal(A2{i, i}, random_A{i, i}), ...
        [BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
        'OrdMxBUT Randomize is not functioning well.')
    end

assert(isequal(numel(find(A2{i, i})), numel(find(random_A{i, i}))), ... % check same number of nodes
[BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
'OrdMxBUT Randomize is not functioning well.')

assert(issymmetric(random_A{i, i}), ... % check symmetry 
[BRAPH2.STR ':OrdMxBUT:' BRAPH2.FAIL_TEST], ...
'OrdMxBUT Randomize is not functioning well.')

end

① same as in Code 12.

%\bibliography{biblio} %\bibliographystyle{plainnat}

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readme.md

Implement a New Graph

Table of Contents

Implementation of unilayer graphs ⬆

Unilayer binary directed graph (`GraphBD`) ⬆

Implementation of multilayer graphs ⬆

Weighted directed multilayer graph (`MultilayerWD`) ⬆

Binary undirected multilayer graph with fixed thresholds (`MultiplexBUT`) ⬆

Binary undirected ordinal multiplex graph with fixed thresholds (`OrdMxBUT`) ⬆

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readme.md

Implement a New Graph

Table of Contents

Implementation of unilayer graphs ⬆

Unilayer binary directed graph (GraphBD) ⬆

Implementation of multilayer graphs ⬆

Weighted directed multilayer graph (MultilayerWD) ⬆

Binary undirected multilayer graph with fixed thresholds (MultiplexBUT) ⬆

Binary undirected ordinal multiplex graph with fixed thresholds (OrdMxBUT) ⬆

Unilayer binary directed graph (`GraphBD`) ⬆

Weighted directed multilayer graph (`MultilayerWD`) ⬆

Binary undirected multilayer graph with fixed thresholds (`MultiplexBUT`) ⬆

Binary undirected ordinal multiplex graph with fixed thresholds (`OrdMxBUT`) ⬆