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ISFCClustering/2019_03_03_BCT/gateway_coef_sign.m
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gateway_coef_sign.m
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function [GWpos,GWneg] = gateway_coef_sign(W,Ci,centtype)
% Gateway coefficient
%
% [Gpos,Gneg] = gateway_coef_sign(W,Ci,centtype);
%
% Gateway coefficient is a variant of participation coefficient. Similar
% to participation coefficient, gateway coefficient measures the
% diversity of intermodular connections of individual nodes, but this is
% weighted by how critical these connections are to intermodular
% connectivity (e.g., if a node is the only connection between it's
% module and another module, it will have a higher gateway coefficient).
%
% Inputs: W, undirected connection matrix with positive and
% negative weights
%
% Ci, community affiliation vector
%
% centtype, centrality measure to use
% 1 = Node Strength
% 2 = Betweenness Centrality
%
% Output: Gpos, gateway coefficient for positive weights
% Gneg, gateway coefficient for negative weights
%
% Reference: Vargas ER, Wahl LM. Eur Phys J B (2014) 87:1-10.
%
% Jeff Spielberg, University of Delaware
% Modification History:
% May 2015: Original (originally adapted from participation_coef_sign.m)
% July 2018: Bugfix, change in how weighted matrices are handled,
% improvements for efficiency, additional line documentation
[~,~,Ci] = unique(Ci); % Remap module indices to consecutive numbers
n = length(W); % Number of nodes
W(1:(n+1):end) = 0; % Ensure diagonal is zero
GWpos = gcoef(W.*(W>0)); % Compute gateway coefficient for positive weights
GWneg = gcoef(-W.*(W<0)); % Compute gateway coefficient for negative weights
function GW = gcoef(W_)
k = sum(W_,2); % Compute node strength
Gc = (W_~=0)*diag(Ci); % Create neighbor community affiliation matrix
nmod = max(Ci); % Find # of modules
ks = zeros(n,nmod); % Preallocate space
kjs = zeros(n,nmod); % Preallocate space
cs = zeros(n,nmod); % Preallocate space
switch centtype % Which centrality measure to use?
case 1 % Node Strength
cent = sum(W_,2);
case 2 % Betweenness Centrality
L = weight_conversion(W_,'lengths');
cent = betweenness_wei(L);
end
mcn = 0; % Set max summed centrality per module to 0
for i = 1:nmod % For each module
if sum(cent(Ci==i))>mcn % If current module has a higher sum
mcn = sum(cent(Ci==i)); % Reassign value
end
ks(:,i) = sum(W_.*(Gc==i),2); % Compute the total weight of the connections per node to each module
end
for i = 1:nmod % For each module
if sum(Ci==i)>1 % If there is more than 1 node in a module
kjs(Ci==i,:) = ones(sum(Ci==i),1)*sum(ks(Ci==i,:)); % Compute total module-module connections
kjs(Ci==i,i) = kjs(Ci==i,i)/2; % Account for redundancy due to double counting within-network work weights
end
end
for i = 1:n % For each node
if k(i)>0 % If node is connected
for ii = 1:nmod % For each module
cs(i,ii) = sum(cent((Ci.*(W_(:,i)>0))==ii)); % Sum of centralities of neighbors of a node within a module
end
end
end
ksm = ks./kjs; % Normalize by total connections
ksm(kjs==0) = 0; % Account for division by 0
csm = cs./mcn; % Normalize by max summed centrality
gs = (1-(ksm.*csm)).^2; % Calculate total weighting
GW = 1-sum((ks.^2)./(k.^2).*gs,2); % Compute gateway coefficient
GW(isnan(GW)) = 0; % Account for division by 0
GW(~GW) = 0; % Set to 0 if no neighbors
end
end
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