GetEdgeEssentiality.m

function [ edge_essen ] = GetEdgeEssentiality(connectivity, y, alpha, w)
%This function computes edge essentialities using network inversion. Given the gene-centric
%essentialities 'y', and the network topology 'connectivity', the interaction essentialities
%are estimated using 
%inputs:
%connectivity - connectivity matrix is an N x M incidence matrix where
%               N and M are the numbers of edges and vertices 
%               respectively, such that connectivity(i,j) = 1 if the 
%               edge ei and vertex vj are incident and 0 otherwise.
%y - a vector of size M representing essentialities of M genes(proteins) 
%alpha - scalar, smoothing parameter used to weight nieghboring essentialities for 
%		each network node when estimating interaction essentialities. A value of '0' means
%		that each node should be handled independently of its neighbors.
%w - scalar, weighting parameter for network inversion. w represents how 
%       much the essentiality of proteins affects the essentiality of interactions
%       in between. Larger values of w show that an interaction is essential 
%       if the corresponding proteins are essential, and smaller values of w show 
%       that no matter how essential the corresponding proteins are the
%       interaction is important.
%outputs:
%edge_essen - a vector of size N indicating essentialities of N
%             interactions of M proteins.

%Licensed to the Apache Software Foundation (ASF) under one
%or more contributor license agreements.  See the NOTICE file
%distributed with this work for additional information
%regarding copyright ownership.  The ASF licenses this file
%to you under the Apache License, Version 2.0 (the
%"License"); you may not use this file except in compliance
%with the License.  You may obtain a copy of the License at
%
%  http://www.apache.org/licenses/LICENSE-2.0
%
%Unless required by applicable law or agreed to in writing,
%software distributed under the License is distributed on an
%"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
%KIND, either express or implied.  See the License for the
%specific language governing permissions and limitations
%under the License.

inds = find(sum(connectivity,2) > 0);
C = connectivity(inds, :);
y = y(inds);

m = size(C,2);

graph_edges= zeros(m,2);
for i=1:m
    nds = find(C(:,i)==1);
    graph_edges(i,1) = nds(1);
    graph_edges(i,2) = nds(2);
end

v_imp = y;

B = C;
M = size(B,2);
N = size(B,1);

G = zeros(M,M);
for u=1:N
    x = find(B(u,:) > 0);
    for i=1:length(x)
        for j=i+1:length(x)
            G(x(i), x(j)) = exp(w*v_imp(u));
            G(x(j), x(i)) =  G(x(i), x(j)) ;
        end
    end
    
end

[~, cc] = graphconncomp(sparse(G), 'Directed', 'false');
large_con = mode(cc);
inds = find(large_con~=cc);
G(:, inds) = [];
G(inds,:) = [];

edge_essen = zeros(M,1);
new_inds = large_con==cc;


GX = diag(1./sum(G))*G;
D = diag(sum(GX,2));
GN = alpha*GX + (1-alpha)*D;


[vv,~] = eigs(GN',1);
vec = vv(:,1);

if(isempty(inds))
    edge_essen(1:end) = vec;
else
    edge_essen(new_inds) = vec;
end
 

end