graph_create.m

function [Adj_VL, Adj_VL_2, Adj, Adj_2] = graph_create(connections, connections_2, N)
%GRAPH_CREATE gives two random graphs using Erdos-Renyi-Algorithm of n-vehicles and
%finds minimum directed spanning tree of these two graphs
%
% Inputs:
%     N            - number of vehicles
%     connections  - to leader connected vehicles in graph 1
%     connections_2- to leader connected vehicles in graph 2
% Outputs:
%     Adj_VL    - Consensus adjacency matrix graph 1 with virtual leader connections
%     Adj_VL_2  - same as above for graph 2
%     Adj       - Adjacency matrix graph 1 without virtual leader
%     Adj_2     - same as above for graph 2

graphs = figure;
scrsz = get(groot, 'ScreenSize');
set(graphs, 'Name', 'Communication Topologies', 'NumberTitle', 'off','OuterPosition',[0 0 scrsz(3)/2 scrsz(4)/2]);

% call erdosRenyi 
G = graph(erdosRenyi(N,0.6), 'upper', 'OmitSelfLoops');
subplot(2,2,1);
p = plot(G);
set(gca,'XTickLabel',[],'YTickLabel',[])

G_2 = graph(erdosRenyi(N,0.6),'upper','OmitSelfLoops');
subplot(2,2,3);
p_2 = plot(G_2);
set(gca,'XTickLabel',[],'YTickLabel',[]);

% find minimum spanning tree from the first element in the connected list
% and create undirected graph from the root of the tree
[T,pred] = minspantree(G,'Type','forest','Root',connections(1));
highlight(p,T)
subplot(2,2,2);
p_3 = plot(T);
set(gca,'XTickLabel',[],'YTickLabel',[])

[T_2,pred_2] = minspantree(G_2,'Type','forest','Root',connections_2(1));
highlight(p_2,T_2)
subplot(2,2,4);
p_4 = plot(T_2);
set(gca,'XTickLabel',[],'YTickLabel',[]);

% creates last column and row for adjacency matrix
connect = connect_VL(connections,N);
connect_2 = connect_VL(connections_2,N);

% creates adjacency matrixes
disp('Adjacency matrixes first graph');
Adj = full(T.adjacency)'
Adj_VL = [Adj connect; connect' 0]
disp('Adjacency matrixes second graph');
Adj_2 = full(T_2.adjacency)'
Adj_VL_2 = [Adj_2 connect_2; connect_2' 0]

end

function [Adj_lColumn] = connect_VL(connections,N)
% creates the last column and row (connections to the VL) of a Adj depending on the
% connections specified
Adj_lColumn = zeros(N,1);
for i=1:1:length(connections)
    Adj_lColumn(connections(i)) = 1;
end
end

function [Adj] = erdosRenyi(N,p)
% creates random adjacency matrix according to Erdos-Renyi algorithm
Adj = triu(rand(N)<p,1); % upper triangular to avoid self-loops
Adj = Adj+Adj';
end