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viewnetworks.m
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viewnetworks.m
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function[Networkdata,Graphdata] = viewnetworks(fig_output,networkparameters,a,timeslices_IBN,timeslices_OPN,UU_adjmats,DW_adjmats,BP_mats,tol)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initializations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fig_output_VN = strcat(fig_output,'Network/');
% Presetting loop parameters for subplots associated to selected timeslices
for i = 1:numel(timeslices_IBN)
Slice_IBN{i} = strcat('Slice',num2str(timeslices_IBN(i)));
graphtitle_IBN{i} = strcat('t = ',num2str(timeslices_IBN(i)));
end
for i = 1:numel(timeslices_OPN)
Slice_OPN{i} = strcat('Slice',num2str(timeslices_OPN(i)));
graphtitle_OPN{i} = strcat('t = ',num2str(timeslices_OPN(i)));
end
adj_mat = UU_adjmats;
diadj_mat = DW_adjmats(:,:,:,1);
loan_mat = DW_adjmats(:,:,:,2);
opnet_mat = BP_mats;
markernorm = networkparameters(1);
edgewnorm = networkparameters(2);
graphlayout = networkparameters(3);
for i = 1:numel(Slice_IBN)
% Bank nodes
Networkdata_nodes.banks.(Slice_IBN{i}).sizes_zero = (a(:,i)./(max(a(:,1))/markernorm)); % Use largest bank at start of simulation to size nodes
Networkdata_nodes.banks.(Slice_IBN{i}).nonzero_ids = find(Networkdata_nodes.banks.(Slice_IBN{i}).sizes_zero~=0);
Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero = Networkdata_nodes.banks.(Slice_IBN{i}).sizes_zero;
Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero(Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero==0) = [];
Networkdata_nodes.banks.(Slice_IBN{i}).numnodes = numel(Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero);
Networkdata_nodes.banks.(Slice_IBN{i}).nodearray = 1:Networkdata_nodes.banks.(Slice_IBN{i}).numnodes;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Undirected, unweighted networks (UUN): Existing relationships between banks
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:numel(Slice_IBN)
Networkdata_UU.(Slice_IBN{i}).adj_mat = adj_mat(find(Networkdata_nodes.banks.(Slice_IBN{i}).sizes_zero),find(Networkdata_nodes.banks.(Slice_IBN{i}).sizes_zero),i);
end
% Initial simulated network
G_UU.(Slice_IBN{1}) = graph(Networkdata_UU.(Slice_IBN{1}).adj_mat);
G_UU.(Slice_IBN{1}).Nodes.Size = Networkdata_nodes.banks.(Slice_IBN{1}).sizes_nozero;
figure
subplot(1,2,1)
h = plot(G_UU.(Slice_IBN{1}),'Layout','force','MarkerSize',Networkdata_nodes.banks.(Slice_IBN{1}).sizes_nozero);
labelnode(h,Networkdata_nodes.banks.(Slice_IBN{1}).nodearray,Networkdata_nodes.banks.(Slice_IBN{1}).nonzero_ids)
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
title('(a) Force layout','Interpreter','latex')
subplot(1,2,2)
h = plot(G_UU.(Slice_IBN{1}),'Layout',graphlayout,'MarkerSize',Networkdata_nodes.banks.(Slice_IBN{1}).sizes_nozero);
labelnode(h,Networkdata_nodes.banks.(Slice_IBN{1}).nodearray,Networkdata_nodes.banks.(Slice_IBN{1}).nonzero_ids)
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
title('(b) Circular layout','Interpreter','latex')
set(gcf,'renderer','painters');
hfig = tightfig;
%set(gcf,'Units','Inches');
%pos = get(gcf,'Position');
%set(gcf,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[pos(3), pos(4)])
print(hfig,'-dpdf',strcat(fig_output_VN,'interbanknetwork_initial.pdf'));
% Evolving network structure at four time points over the simulation figure
figure
for i = 2:numel(Slice_IBN)
subplot(2,2,i-1)
G_UU.(Slice_IBN{i}) = graph(Networkdata_UU.(Slice_IBN{i}).adj_mat);
G_UU.(Slice_IBN{i}).Nodes.Size = Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero;
h = plot(G_UU.(Slice_IBN{i}),'Layout',graphlayout,'MarkerSize',Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero);
labelnode(h,Networkdata_nodes.banks.(Slice_IBN{i}).nodearray,Networkdata_nodes.banks.(Slice_IBN{i}).nonzero_ids)
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
title(graphtitle_IBN{i},'Interpreter','latex')
end
set(gcf,'renderer','painters');
hfig = tightfig;
%set(gcf,'Units','Inches');
%pos = get(gcf,'Position');
%set(gcf,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[pos(3), pos(4)])
print(hfig,'-dpdf',strcat(fig_output_VN,'interbanknetwork_evolution.pdf'));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Directed, Weighted networks: Interbank market dynamics
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:numel(Slice_IBN)
Networkdata_DW.(Slice_IBN{i}).diadj_mat = diadj_mat(:,:,i);
Networkdata_DW.(Slice_IBN{i}).loan_mat = loan_mat(:,:,i);
Networkdata_DW.(Slice_IBN{i}).edgelist = adj2edgeL(diadj_mat(:,:,i));
if ~isempty(Networkdata_DW.(Slice_IBN{i}).edgelist)
Networkdata_DW.(Slice_IBN{i}).srcnodes = Networkdata_DW.(Slice_IBN{i}).edgelist(:,1);
Networkdata_DW.(Slice_IBN{i}).ternodes = Networkdata_DW.(Slice_IBN{i}).edgelist(:,2);
Networkdata_DW.(Slice_IBN{i}).activenodes = unique([Networkdata_DW.(Slice_IBN{i}).srcnodes; Networkdata_DW.(Slice_IBN{i}).ternodes]);
Networkdata_DW.(Slice_IBN{i}).numactivenodes = numel(Networkdata_DW.(Slice_IBN{i}).activenodes);
Networkdata_DW.(Slice_IBN{i}).activenodearray = 1:numel(Networkdata_DW.(Slice_IBN{i}).activenodes);
Networkdata_DW.(Slice_IBN{i}).idx = sub2ind(size(Networkdata_DW.(Slice_IBN{i}).diadj_mat),...
Networkdata_DW.(Slice_IBN{i}).srcnodes,Networkdata_DW.(Slice_IBN{i}).ternodes);
Networkdata_DW.(Slice_IBN{i}).weights = Networkdata_DW.(Slice_IBN{i}).loan_mat(Networkdata_DW.(Slice_IBN{i}).idx);
Networkdata_DW.(Slice_IBN{i}).edgewidths = edgewnorm*Networkdata_DW.(Slice_IBN{i}).weights/max(Networkdata_DW.(Slice_IBN{i}).weights);
end
end
Networkdata.nodes = Networkdata_nodes.banks;
Networkdata.UU = Networkdata_UU;
Networkdata.DW = Networkdata_DW;
% 1st period interbank dynamics
G_DW.(Slice_IBN{1}) = digraph(Networkdata_DW.(Slice_IBN{1}).srcnodes,Networkdata_DW.(Slice_IBN{1}).ternodes,Networkdata_DW.(Slice_IBN{1}).weights);
G_DW.(Slice_IBN{1}) = rmnode(G_DW.(Slice_IBN{1}),setdiff(Networkdata_nodes.banks.(Slice_IBN{1}).nodearray,Networkdata_DW.(Slice_IBN{1}).activenodes));
G_DW.(Slice_IBN{1}).Nodes.Size = Networkdata_nodes.banks.(Slice_IBN{1}).sizes_zero(Networkdata_DW.(Slice_IBN{1}).activenodes);
figure
subplot(1,2,1)
h = plot(G_DW.(Slice_IBN{1}),'Layout','force','LineWidth',Networkdata_DW.(Slice_IBN{1}).edgewidths,'MarkerSize',G_DW.(Slice_IBN{1}).Nodes.Size);
labelnode(h,Networkdata_DW.(Slice_IBN{1}).activenodearray,Networkdata_DW.(Slice_IBN{1}).activenodes)
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
title('(a) Force layout','Interpreter','latex')
subplot(1,2,2)
h = plot(G_DW.(Slice_IBN{1}),'Layout',graphlayout,'LineWidth',Networkdata_DW.(Slice_IBN{1}).edgewidths,'MarkerSize',G_DW.(Slice_IBN{1}).Nodes.Size);
labelnode(h,Networkdata_DW.(Slice_IBN{1}).activenodearray,Networkdata_DW.(Slice_IBN{1}).activenodes)
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
title('(b) Circular layout','Interpreter','latex')
set(gcf,'renderer','painters');
hfig = tightfig;
%set(gcf,'Units','Inches');
%pos = get(gcf,'Position');
%set(gcf,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[pos(3), pos(4)])
print(hfig,'-dpdf',strcat(fig_output_VN,'interbankloans_initial.pdf'));
% Interbank dynamics for selected $timeslices$
figure
for i = 2:numel(Slice_IBN)
subplot(2,numel(Slice_IBN)-3,i-1)
if ~isempty(Networkdata_DW.(Slice_IBN{i}).edgelist)
G_DW.(Slice_IBN{i}) = digraph(Networkdata_DW.(Slice_IBN{i}).srcnodes,Networkdata_DW.(Slice_IBN{i}).ternodes,Networkdata_DW.(Slice_IBN{i}).weights);
G_DW.(Slice_IBN{i}) = rmnode(G_DW.(Slice_IBN{i}),setdiff(Networkdata_nodes.banks.(Slice_IBN{1}).nodearray,Networkdata_DW.(Slice_IBN{i}).activenodes));
G_DW.(Slice_IBN{i}).Nodes.Size = Networkdata_nodes.banks.(Slice_IBN{i}).sizes_zero(Networkdata_DW.(Slice_IBN{i}).activenodes);
% Networkdata_DW.(Slice{i}).activenodes
%G_DW.(Slice{i}).Nodes.Size
h = plot(G_DW.(Slice_IBN{i}),'Layout',graphlayout,'LineWidth',Networkdata_DW.(Slice_IBN{i}).edgewidths,'MarkerSize',G_DW.(Slice_IBN{i}).Nodes.Size+tol);
labelnode(h,Networkdata_DW.(Slice_IBN{i}).activenodearray,Networkdata_DW.(Slice_IBN{i}).activenodes)
else
h = plot(G_UU.(Slice_IBN{i}),'Layout',graphlayout,'MarkerSize',Networkdata_nodes.banks.(Slice_IBN{i}).sizes_nozero);
labelnode(h,Networkdata_nodes.banks.(Slice_IBN{i}).nodearray,Networkdata_nodes.banks.(Slice_IBN{i}).nonzero_ids)
end
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
title(graphtitle_IBN{i},'Interpreter','latex')
end
set(gcf,'renderer','painters');
hfig = tightfig;
%set(gcf,'Units','Inches');
%pos = get(gcf,'Position');
%set(gcf,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[pos(3), pos(4)])
print(hfig,'-dpdf',strcat(fig_output_VN,'interbankloans_evolution.pdf'));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Weighted bipartite graph: Overlapping portfolio dynamics
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i = 1:numel(Slice_OPN)
Networkdata_BP.(Slice_OPN{i}).opnet_mat_zero = opnet_mat(:,:,i);
Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero = Networkdata_BP.(Slice_OPN{i}).opnet_mat_zero;
Networkdata_BP.(Slice_OPN{i}).bankids = find(sum(Networkdata_BP.(Slice_OPN{i}).opnet_mat_zero,2)~=0);
Networkdata_BP.(Slice_OPN{i}).assetids = find(sum(Networkdata_BP.(Slice_OPN{i}).opnet_mat_zero,1)~=0);
Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero(~any(Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero,2),:) = [];
Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero(:,~any(Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero,1)) = [];
Networkdata_BP.(Slice_OPN{i}).numbanks = size(Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero,1);
Networkdata_BP.(Slice_OPN{i}).bankarray = 1:size(Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero,1);
Networkdata_BP.(Slice_OPN{i}).numassets = size(Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero,2);
Networkdata_BP.(Slice_OPN{i}).assetarray = 1:size(Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero,2);
% Represent bipartite graph as an [N+M]x[N+M] adjacency matrix
% Populate TL quadrant: ZERO MATRIX - Banks in bipartite graph are not connected - NxN
Networkdata_BP.(Slice_OPN{i}).opvizmat(Networkdata_BP.(Slice_OPN{i}).bankarray,...
Networkdata_BP.(Slice_OPN{i}).bankarray) = zeros(Networkdata_BP.(Slice_OPN{i}).numbanks);
% Populate BR quadrant: ZERO MATRIX - Assets in bipartite graph are not connected - MxM
Networkdata_BP.(Slice_OPN{i}).opvizmat(Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks + Networkdata_BP.(Slice_OPN{i}).numassets),...
Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks+Networkdata_BP.(Slice_OPN{i}).numassets)) = ...
zeros(Networkdata_BP.(Slice_OPN{i}).numassets);
% Populate BL quadrant: Asset-Bank links - MxN
Networkdata_BP.(Slice_OPN{i}).opvizmat(Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks+Networkdata_BP.(Slice_OPN{i}).numassets),...
Networkdata_BP.(Slice_OPN{i}).bankarray) = (Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero)';
% Populate TR quadrant: Bank-Asset links - NxM
Networkdata_BP.(Slice_OPN{i}).opvizmat(Networkdata_BP.(Slice_OPN{i}).bankarray,...
Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks+Networkdata_BP.(Slice_OPN{i}).numassets)) =...
Networkdata_BP.(Slice_OPN{i}).opnet_mat_nozero;
end
% Initial overlapping portfolio network
G_BP.(Slice_OPN{1}) = graph(Networkdata_BP.(Slice_OPN{1}).opvizmat);
figure
h=plot(G_BP.(Slice_OPN{1}));
% Assets represented in red
highlight(h,Networkdata_BP.(Slice_OPN{1}).numbanks+1:(Networkdata_BP.(Slice_OPN{1}).numbanks+Networkdata_BP.(Slice_OPN{1}).numassets),'NodeColor','r');
% Labelling active BANKS
labelnode(h,Networkdata_BP.(Slice_OPN{1}).bankarray,Networkdata_BP.(Slice_OPN{1}).bankids)
% Labelling active ASSETS
labelnode(h,Networkdata_BP.(Slice_OPN{1}).numbanks+1:Networkdata_BP.(Slice_OPN{1}).numbanks+Networkdata_BP.(Slice_OPN{1}).numassets,...
Networkdata_BP.(Slice_OPN{1}).assetids)
% Reorganising to visualise as bipartite graph
%%% Banks on LHS
h.XData(1:Networkdata_BP.(Slice_OPN{1}).numbanks) = 1;
h.YData(1:Networkdata_BP.(Slice_OPN{1}).numbanks) = linspace(0,1,Networkdata_BP.(Slice_OPN{1}).numbanks);
%h.YData(1:Networkdata_BP.(Slice{1}).numbanks) = linspace(0.5-(Networkdata_BP.(Slice{1}).numbanks/(2*Networkdata_BP.(Slice{1}).numassets)),...
%0.5+(Networkdata_BP.(Slice{1}).numbanks/(2*Networkdata_BP.(Slice{1}).numassets)),Networkdata_BP.(Slice{1}).numbanks);
%%% Assets on RHS
h.XData(Networkdata_BP.(Slice_OPN{1}).numbanks+1:(Networkdata_BP.(Slice_OPN{1}).numbanks+Networkdata_BP.(Slice_OPN{1}).numassets)) = 2;
h.YData(Networkdata_BP.(Slice_OPN{1}).numbanks+1:(Networkdata_BP.(Slice_OPN{1}).numbanks+Networkdata_BP.(Slice_OPN{1}).numassets))...
= linspace(0,1,Networkdata_BP.(Slice_OPN{1}).numassets);
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
set(gcf,'renderer','painters');
hfig = tightfig;
%set(gcf,'Units','Inches');
%pos = get(gcf,'Position');
%set(gcf,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[pos(3), pos(4)])
print(hfig,'-dpdf',strcat(fig_output_VN,'overlappingportfolio_initial.pdf'));
% Overlapping portfolio network evolution
figure
for i = 2:numel(Slice_OPN)
subplot(3,numel(Slice_OPN)-5,i-1)
G_BP.(Slice_OPN{i}) = graph(Networkdata_BP.(Slice_OPN{i}).opvizmat);
h=plot(G_BP.(Slice_OPN{i}),'NodeLabel',[]);
highlight(h,Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks+Networkdata_BP.(Slice_OPN{i}).numassets),'NodeColor','r');
%labelnode(h,Networkdata_BP.(Slice{i}).bankarray,Networkdata_BP.(Slice{i}).bankids)
%labelnode(h,Networkdata_BP.(Slice{i}).numbanks+1:Networkdata_BP.(Slice{i}).numbanks+Networkdata_BP.(Slice{i}).numassets,...
%Networkdata_BP.(Slice{i}).assetids)
% Reorganising to visualise as bipartite graph
h.XData(1:Networkdata_BP.(Slice_OPN{i}).numbanks) = 1;
%h.YData(1:Networkdata_BP.(Slice{i}).numbanks) = linspace(0.5-(Networkdata_BP.(Slice{i}).numbanks/(2*Networkdata_BP.(Slice{i}).numassets)),...
%0.5+(Networkdata_BP.(Slice{i}).numbanks/(2*Networkdata_BP.(Slice{i}).numassets)),Networkdata_BP.(Slice{i}).numbanks);
h.YData(1:Networkdata_BP.(Slice_OPN{i}).numbanks) = linspace(0,1,Networkdata_BP.(Slice_OPN{i}).numbanks);
h.XData(Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks+Networkdata_BP.(Slice_OPN{i}).numassets)) = 2;
h.YData(Networkdata_BP.(Slice_OPN{i}).numbanks+1:(Networkdata_BP.(Slice_OPN{i}).numbanks+Networkdata_BP.(Slice_OPN{i}).numassets))...
= linspace(0,1,Networkdata_BP.(Slice_OPN{i}).numassets);
title(graphtitle_OPN{i},'Interpreter','latex')
set(gca,'XLim',[1 2],'YLim',[0 1])
set(gca,'XtickLabel',[],'YtickLabel',[],'XTick',[],'YTick',[]);
end
set(gcf,'renderer','painters');
%hfig = tightfig;
%set(gcf,'Units','Inches');
%pos = get(hfig,'Position');
set(gcf,'Units', 'Centimeters', 'Position', [0, 0, 18, 23],'PaperUnits','Centimeters','PaperSize',[18,23])
%set(hfig,'PaperPositionMode','Auto','PaperUnits','Inches','PaperSize',[pos(3), pos(4)])
print(gcf,'-dpdf',strcat(fig_output_VN,'overlappingportfolio_evolution.pdf'));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Output collected network information
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Networkdata.nodes = Networkdata_nodes.banks;
Networkdata.UU = Networkdata_UU;
Networkdata.DW = Networkdata_DW;
Networkdata.BP = Networkdata_BP;
Graphdata.UU = G_UU;
Graphdata.DW = G_DW;
Graphdata.BP = G_BP;
end