(* ::Package:: *)

Needs["ErrorBarPlots`"]


(* ::Section:: *)
(*Visualize graphs*)


gsraw=Import[NotebookDirectory[]<>"graphdata.m"];


ListPlot[gsraw[[2]],Joined->True,PlotRange->All,AxesLabel->{"Step","Triangles"}]


gs=Map[Graph[#,GraphLayout->"CircularEmbedding"]&,gsraw[[1]]];
gs2=Map[Graph[#,GraphLayout->Automatic]&,gsraw[[1]]];


Grid[Partition[gs,10],Frame->All]


(* ::Section:: *)
(*Plot triangle counts*)


(* ::Subsection:: *)
(*Data import and data merge*)


gsraw=Import[NotebookDirectory[]<>"graphdata_merged.m"];


newData=Import[NotebookDirectory[]<>"graphdata_tau_multi3.m"];
mergedData=Import[NotebookDirectory[]<>"graphdata_merged.m"];
Export[NotebookDirectory[]<>"graphdata_merged_new.m",Join[mergedData,newData]]


(* ::Subsection:: *)
(*Plot empirical distribution of maximum degree*)


maxDegrees=Map[{#[[1]],Max[#[[3]]]}&,gsraw];
maxDegrees=GatherBy[maxDegrees,{#[[1,2]]&,#[[1,1]]&}];


Histogram[maxDegrees[[1,-1,All,2]],PlotRange->{{0,1100},{0,200}},AxesLabel->{"d_max","frequency"}]
Histogram[maxDegrees[[2,-1,All,2]],PlotRange->{{0,1100},{0,200}},AxesLabel->{"d_max","frequency"}]
Histogram[maxDegrees[[3,-1,All,2]],PlotRange->{{0,1100},{0,200}},AxesLabel->{"d_max","frequency"}]


(* ::Subsection:: *)
(*Plot triangle count over "time" in Markov chain instances*)


numPlots=10;
minCount=Min[Map[Min[#[[2]]]&,gsraw[[1;;numPlots]]]];
maxCount=Max[Map[Max[#[[2]]]&,gsraw[[1;;numPlots]]]];
maxTime=Max[Map[Length[#[[2]]]&,gsraw[[1;;numPlots]]]];
skipPts=Round[maxTime/100]; (* Plotting every point is slow. Plot only once per `skipPts` timesteps *)
coarseData=Map[#[[2,1;;-1;;skipPts]]&,gsraw[[1;;numPlots]]];
labels=Map["{n,tau} = "<>ToString[#[[1]]]&,gsraw[[1;;numPlots]]];
ListPlot[coarseData,Joined->True,PlotRange->{minCount,maxCount},DataRange->{0,maxTime},PlotLegends->labels]
(* Map[ListPlot[#,Joined->True,PlotRange\[Rule]{minCount,maxCount},DataRange\[Rule]{0,maxTime}]&,coarseData] *)


(* ::Subsection:: *)
(*Plot average #triangles vs n*)


averages=Map[{#[[1]],Mean[#[[2,1;;-1]]]}&,gsraw];
averagesGrouped=GatherBy[averages,{#[[1,1]]&,#[[1,2]]&}];
(* averagesGroupes[[ n index, tau index , run index, {ntau, tri, ds} ]] *)
averagesGrouped=Transpose[averagesGrouped];
(* averagesGrouped[[ tau index, n index, run index ]] *)
nlabels=Map["n = "<>ToString[#]&,averagesGrouped[[1,All,1,1,1]]];
taulabels=Map["tau = "<>ToString[#]&,averagesGrouped[[All,1,1,1,2]]];
averagesErrorBars=Map[
{{#[[1,1,1]],Mean[#[[All,2]]]},
ErrorBar[StandardDeviation[#[[All,2]]]/Sqrt[Length[#]]]
}&,averagesGrouped,{2}];


ErrorListPlot[averagesErrorBars,Joined->True,PlotMarkers->Automatic,AxesLabel->{"n","\[LeftAngleBracket]triangles\[RightAngleBracket]"},PlotLegends->taulabels]


(* ::Subsection:: *)
(*Plot #triangles distribution for specific (n,tau)*)


histograms=Map[Histogram[#[[All,2]]]&,averagesGrouped,{2}];
nlabels=Map["n = "<>ToString[#]&,averagesGrouped[[1,All,1,1,1]]];
taulabels=Map["tau = "<>ToString[#]&,averagesGrouped[[All,1,1,1,2]]];


TableForm[histograms,TableHeadings->{taulabels,nlabels}]