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We are grateful to Francesc Comellas for letting us \ know that the mentioned functions were not working properly in version 1.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Packages", "Section"], Cell[BoxData[ \(\(\(\(Needs["\"];\)\ (*\ For\ the\ analysis\ of\ \(\(graphs\)\(.\)\)\ *) \[IndentingNewLine] \(Needs["\"];\)\ (*\ For\ the\ \(\(Histograms\)\(.\)\)\ *) \[IndentingNewLine] \(Needs["\"];\)\)\(\ \)\( (*\ For\ Frequencies, \ used\ in\ the\ function\ \(\(ReachabilityCloseness\)\(.\)\)\ *) \ \)\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Functions", "Section"], Cell[BoxData[{ \(\(Off[General::spell];\)\ \[IndentingNewLine]\[IndentingNewLine] (*\ This\ function\ returns\ the\ number\ of\ reciprocated\ links\ in\ a\ \ simple\ \(\(network\)\(.\)\)\ *) \), "\[IndentingNewLine]", \(\(ReciprocatedEdges[g_Graph] := Module[{adjMatrix = ToAdjacencyMatrix[g]}, Count[adjMatrix + Transpose[adjMatrix], 2, {2}]];\)\[IndentingNewLine]\[IndentingNewLine] (*\ A\ clique\ is\ a\ subset\ of\ the\ vertices\ such\ that\ every\ pair\ \ of\ vertices\ in\ the\ subset\ is\ connected\ by\ an\ edge . \ This\ function\ returns\ a\ clique\ of\ maximum\ size\ allowing\ \ for\ paths\ of\ any\ length\ no\ greater\ than\ n, \ i . e . \ an\ n - clique\ *) \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(MaximumNClique[g_Graph, n_Integer] := MaximumClique[ RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[g, n]]]];\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine] (*\ Returns\ true\ if\ c\ is\ an\ n - clique, \ i . e . \ allowing\ for\ paths\ of\ any\ length\ no\ greater\ than\ n . \ False\ \(\(otherwise\)\(.\)\)\ *) \[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(NCliqueQ[g_Graph, n_Integer, c_List] := CliqueQ[RemoveSelfLoops[RemoveMultipleEdges[GraphPower[g, n]]], c];\)\[IndentingNewLine]\[IndentingNewLine] (*\ An\ n - clan\ is\ an\ n - clique\ where\ all\ ties\ among\ members\ of\ the\ n - clique\ occur\ through\ members\ of\ the\ n - clique . \ This\ function\ returns\ a\ list\ of\ all\ the\ n - clans\ of\ maximum\ size, \ i . e . \ allowing\ for\ paths\ of\ any\ length\ no\ greater\ than\ \ \(\(n\)\(.\)\)\ *) \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(MaximumNClans[g_Graph, n_Integer] := Module[{listOfDegrees, allSuitableNodes = Range[V[g]], clans = {}}, \[IndentingNewLine]\[IndentingNewLine] (*\ A\ clan\ is, \ in\ particular, \ a\ clique, \ so\ find\ out\ the\ maximum\ possible\ size\ of\ the\ \ \(\(clan\)\(.\)\)\ *) \[IndentingNewLine]maxSizeOfClan = Length[MaximumNClique[g, n]]; \[IndentingNewLine]\[IndentingNewLine] (*\ There\ is\ no\ need\ to\ consider\ the\ nodes\ of\ degree\ \ maxSizeOfClan - 2\ or\ less\ \((in\ the\ powered\ graph)\)\ as\ they\ cannot\ \ be\ part\ of\ an\ n - clique\ or\ an\ n - \(\(clan\)\(.\)\)\ \ *) \[IndentingNewLine]listOfDegrees = Degrees[RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[g, n]]]]; \[IndentingNewLine]allSuitableNodes = Select[allSuitableNodes, \ \((listOfDegrees[\([#]\)] \ \[GreaterEqual] \ maxSizeOfClan - 1)\) &]; \[IndentingNewLine]\[IndentingNewLine]While[ Length[clans] \[Equal] 0\ && \ maxSizeOfClan \[GreaterEqual] \ 1, \[IndentingNewLine]possibleClans = Subsets[allSuitableNodes, {maxSizeOfClan}]; \ \[IndentingNewLine]clans = Select[possibleClans, CompleteQ[ RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[InduceSubgraph[g, #], n]]]] &]; \[IndentingNewLine]\(maxSizeOfClan--\);\ \[IndentingNewLine]]; \[IndentingNewLine]\[IndentingNewLine]clans\ \[IndentingNewLine]];\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine] (*\ Returns\ true\ if\ c\ is\ an\ n - clan, \ i . e . \ allowing\ for\ paths\ of\ any\ length\ no\ greater\ than\ n . \ False\ \(\(otherwise\)\(.\)\)\ *) \[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(NClanQ[g_Graph, n_Integer, c_List] := CompleteQ[ RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[InduceSubgraph[g, c], n]]]];\)\[IndentingNewLine]\[IndentingNewLine] (*\ The\ clustering\ coefficient\ of\ a\ node\ is\ the\ ratio\ of\ existing\ \ links\ connecting\ the\ node' s\ neighbours\ to\ each\ other, to\ the\ maximum\ possible\ number\ of\ such\ links . \ For\ nodes\ with\ fewer\ than\ two\ neighbours\ the\ clustering\ \ coefficient\ is\ \(\(undefined\)\(.\)\)*) \[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(Clustering[v_Integer, g_Graph] := Module[\[IndentingNewLine]{nbrs, subGraph}, \[IndentingNewLine]\[IndentingNewLine]nbrs = Complement[Neighborhood[g, v, 1], {v}]; \[IndentingNewLine]If[ Length[nbrs] < 2, Return["\"]]; \ \[IndentingNewLine]\[IndentingNewLine]subGraph = InduceSubgraph[g, nbrs]; \[IndentingNewLine]\[IndentingNewLine]If[ UndirectedQ[g], \[IndentingNewLine]Return[ 2*M[subGraph]/\((V[ subGraph]*\((V[subGraph] - 1)\))\)], \[IndentingNewLine]Return[ M[subGraph]/\((V[ subGraph]*\((V[subGraph] - 1)\))\)]\[IndentingNewLine]];\[IndentingNewLine]];\)\ \[IndentingNewLine]\n (*\ An\ n - clan\ is\ an\ n - clique\ where\ all\ ties\ among\ members\ of\ the\ n - clique\ occur\ through\ members\ of\ the\ n - clique . \ This\ function\ returns\ a\ list\ of\ all\ the\ n - clans\ of\ maximum\ size, \ i . e . \ allowing\ for\ paths\ of\ any\ length\ no\ greater\ than\ \ \(\(n\)\(.\)\)\ *) \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(MaximumNClans[g_Graph, n_Integer] := Module[{listOfDegrees, allSuitableNodes = Range[V[g]], clans = {}}, \[IndentingNewLine]\[IndentingNewLine] (*\ A\ clan\ is, \ in\ particular, \ a\ clique, \ so\ find\ out\ the\ maximum\ possible\ size\ of\ the\ \ \(\(clan\)\(.\)\)\ *) \[IndentingNewLine]maxSizeOfClan = Length[MaximumNClique[g, n]]; \[IndentingNewLine]\[IndentingNewLine] (*\ There\ is\ no\ need\ to\ consider\ the\ nodes\ of\ degree\ \ maxSizeOfClan - 2\ or\ less\ \((in\ the\ powered\ graph)\)\ as\ they\ cannot\ \ be\ part\ of\ an\ n - clique\ or\ an\ n - \(\(clan\)\(.\)\)\ \ *) \[IndentingNewLine]listOfDegrees = Degrees[RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[g, n]]]]; \[IndentingNewLine]allSuitableNodes = Select[allSuitableNodes, \ \((listOfDegrees[\([#]\)] \ \[GreaterEqual] \ maxSizeOfClan - 1)\) &]; \[IndentingNewLine]\[IndentingNewLine]While[ Length[clans] \[Equal] 0\ && \ maxSizeOfClan \[GreaterEqual] \ 1, \[IndentingNewLine]possibleClans = Subsets[allSuitableNodes, {maxSizeOfClan}]; \ \[IndentingNewLine]clans = Select[possibleClans, CompleteQ[ RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[InduceSubgraph[g, #], n]]]] &]; \[IndentingNewLine]\(maxSizeOfClan--\);\ \[IndentingNewLine]]; \[IndentingNewLine]\[IndentingNewLine]clans\ \[IndentingNewLine]];\)\[IndentingNewLine]\[IndentingNewLine] (*\ Returns\ true\ if\ c\ is\ an\ n - clan, \ i . e . \ allowing\ for\ paths\ of\ any\ length\ no\ greater\ than\ n . \ False\ \(\(otherwise\)\(.\)\)\ *) \[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(NClanQ[g_Graph, n_Integer, c_List] := CompleteQ[ RemoveSelfLoops[ RemoveMultipleEdges[ GraphPower[InduceSubgraph[g, c], n]]]];\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine] (*\ The\ clustering\ coefficient\ of\ a\ node\ is\ the\ ratio\ of\ existing\ \ links\ connecting\ the\ node' s\ neighbours\ to\ each\ other, to\ the\ maximum\ possible\ number\ of\ such\ links . \ For\ nodes\ with\ fewer\ than\ two\ neighbours\ the\ clustering\ \ coefficient\ is\ \(\(undefined\)\(.\)\)*) \[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(Clustering[v_Integer, g_Graph] := Module[\[IndentingNewLine]{nbrs, subGraph}, \[IndentingNewLine]\[IndentingNewLine]nbrs = Complement[Neighborhood[g, v, 1], {v}]; \[IndentingNewLine]If[ Length[nbrs] < 2, Return["\"]]; \ \[IndentingNewLine]\[IndentingNewLine]subGraph = InduceSubgraph[g, nbrs]; \[IndentingNewLine]\[IndentingNewLine]If[ UndirectedQ[g], \[IndentingNewLine]Return[ 2*M[subGraph]/\((V[ subGraph]*\((V[subGraph] - 1)\))\)], \[IndentingNewLine]Return[ M[subGraph]/\((V[ subGraph]*\((V[subGraph] - 1)\))\)]\[IndentingNewLine]];\[IndentingNewLine]];\)\ \[IndentingNewLine]\[IndentingNewLine] (*\ This\ function\ returns\ a\ list\ of\ 2 - dimensional\ vectors . \ The\ first\ component\ of\ each\ vector\ is\ a\ number\ nbrs\ \ denoting\ a\ number\ of\ neighbours . \ The\ second\ component\ is\ the\ average\ number\ of\ edges\ \ between\ the\ neighbours\ of\ every\ node\ that\ has\ nbrs\ neighbours . \ It\ works\ for\ both\ directed\ and\ undirected\ \ \(\(graphs\)\(.\)\)\ *) \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(Clustering[g_Graph] := Module[\[IndentingNewLine]{listOfNeighbourhoods, listOfNeighbourhoodsGreaterThan1, listOfSubgraphs, myClusteringList, nOfNbrs, listOfDiffOutDegress, totalNumEdges}, \ \[IndentingNewLine]\[IndentingNewLine]listOfNeighbourhoods = Map[Complement[Neighborhood[g, #, 1], {#}] &, Range[V[g]]]; \ \[IndentingNewLine]listOfNeighbourhoodsGreaterThan1 = Select[listOfNeighbourhoods, \((Length[#] > 1)\) &]; \[IndentingNewLine]listOfSubgraphs = Map[InduceSubgraph[g, #] &, listOfNeighbourhoodsGreaterThan1]; \[IndentingNewLine]\ \[IndentingNewLine] (*\ myClusteringList\ is\ a\ list\ of\ two\ elements\ for\ each\ node\ \ with\ 2\ or\ more\ neighbours . \ The\ first\ element\ of\ the\ list\ is\ the\ number\ of\ \ neighbours, \ and\ the\ second\ element\ is\ the\ number\ of\ edges\ between\ \ the\ neighbours . \ It\ works\ for\ both\ directed\ and\ undirected\ \(\(graphs\)\ \(.\)\)\ *) \[IndentingNewLine]myClusteringList = Map[{V[#], M[#]} &, listOfSubgraphs]; \[IndentingNewLine]\[IndentingNewLine]nOfNbrs \ = Length[listOfNeighbourhoodsGreaterThan1]; \ \[IndentingNewLine]listOfDiffOutDegress = Union[myClusteringList[\([All, 1]\)]]; \[IndentingNewLine]totalNumEdges = Table[0, {Length[ listOfDiffOutDegress]}]; \n\[IndentingNewLine]For[i = 1, i \[LessEqual] nOfNbrs, \(i++\), \ \[IndentingNewLine]\(totalNumEdges[\([\(Position[listOfDiffOutDegress, myClusteringList[\([i, 1]\)], 1, 1]\)[\([1, 1]\)]]\)] += myClusteringList[\([i, 2]\)];\)\[IndentingNewLine]]; \n\[IndentingNewLine]If[ UndirectedQ[g], \[IndentingNewLine]Inner[List, listOfDiffOutDegress, \ 2*totalNumEdges/\((listOfDiffOutDegress*\((listOfDiffOutDegress \ - 1)\)*Map[Count[myClusteringList[\([All, 1]\)], #] &, listOfDiffOutDegress])\), List], \[IndentingNewLine]Inner[List, listOfDiffOutDegress, \ totalNumEdges/\((listOfDiffOutDegress*\((listOfDiffOutDegress - 1)\)*Map[Count[myClusteringList[\([All, 1]\)], #] &, listOfDiffOutDegress])\), List], \[IndentingNewLine]]\[IndentingNewLine]];\)\ \[IndentingNewLine]\[IndentingNewLine] (*\ The\ closeness\ centrality\ of\ a\ node\ using\ geodesic\ distance\ is\ \ the\ reciprocal\ of\ the\ sum\ of\ geodesic\ distances\ from\ the\ node\ to\ \ all\ other\ vertices\ in\ the\ graph . \ This\ function\ returns\ the\ closeness\ centrality\ using\ \ geodesic\ distance\ of\ every\ node\ in\ the\ \(\(graph\)\(.\)\)\ *) \ \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(GeodesicCloseness[g_Graph] := 1/Total[AllPairsShortestPath[ g]];\)\[IndentingNewLine]\[IndentingNewLine]\[IndentingNewLine] \ (*\ This\ function\ returns\ a\ list\ with\ the\ reachability\ closeness\ of\ \ each\ node\ in\ the\ graph . \ The\ reachability\ closeness\ of\ a\ node\ is\ calculated\ by\ \ summing\ up\ the\ proportion\ of\ other\ nodes\ reached\ \((for\ the\ first\ \ time)\)\ at\ a\ given\ distance, appropriately\ weighted . \ In\ this\ case\ the\ weights\ used\ are\ 1/ n\ where\ n\ denotes\ the\ distance\ between\ the\ nodes \((e g . \ 1\ for\ nodes\ at\ distance\ 1, \ \.bd\ for\ nodes\ at\ \ distance\ 2 \[Ellipsis])\)\ *) \[IndentingNewLine]\), "\[IndentingNewLine]", \ \(\(ReachabilityCloseness[g_Graph] := Module[{freqLists}, \[IndentingNewLine]freqLists = Map[Rest[Frequencies[#]] &, AllPairsShortestPath[ g]]; \[IndentingNewLine]Map[\((Total[#[\([All, 1]\)]*\((1/#[\([All, 2]\)])\)])\) &, freqLists]/\((V[g] - 1)\)\[IndentingNewLine]];\)\[IndentingNewLine]\ \[IndentingNewLine] (*\ This\ function\ returns\ a\ matrix\ indicating\ the\ number\ of\ \ shortest\ paths\ between\ any\ two\ nodes\ in\ the\ \(\(network\)\(.\)\)*) \ \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(Options[ NumberOfShortestPaths] = {CheckGraphIsConnected \[Rule] True};\)\), "\[IndentingNewLine]", \(\(NumberOfShortestPaths[g_Graph, opts___?OptionQ] := Module[\[IndentingNewLine]{distancesMatrix\ , adjMatrix\ , powersOfAdjMatrix\ }, \ \[IndentingNewLine]\[IndentingNewLine]checkForConnected = CheckGraphIsConnected /. Flatten[{opts, Options[NumberOfShortestPaths]}]; \[IndentingNewLine] (*\ Replace\ \(( /. )\)\ returns\ the\ result\ from\ using\ the\ \ first\ rule\ that\ \(\(applies\)\(.\)\)\ *) \[IndentingNewLine]If[ checkForConnected, \[IndentingNewLine]\(If[\((UndirectedQ[ g]\ && \ \(! ConnectedQ[ g]\))\)\ || \ \((\(! UndirectedQ[ g]\)\ && \ \(! ConnectedQ[g, Strong]\))\), \ \[IndentingNewLine]Print["\"]; \ Return[];\[IndentingNewLine]];\)\[IndentingNewLine]]; \ \[IndentingNewLine]\[IndentingNewLine]distancesMatrix\ = \ AllPairsShortestPath[g]; \[IndentingNewLine]If[ Not[checkForConnected], distancesMatrix = Replace[distancesMatrix, \[Infinity] \[Rule] 0, {2}]]; \[IndentingNewLine] (*\ A\ distance\ of\ 0\ will\ give\ 0\ shortest\ paths\ between\ \ those\ \(\(nodes\)\(.\)\)\ *) \[IndentingNewLine]\[IndentingNewLine]adjMatrix\ \ = \ ToAdjacencyMatrix[g]; \[IndentingNewLine]powersOfAdjMatrix\ = \ NestList[\((# . adjMatrix)\) &, adjMatrix, Max[distancesMatrix] - 1]; \[IndentingNewLine]\[IndentingNewLine]PrependTo[ powersOfAdjMatrix, Table[0, {V[g]}, {V[g]}]]; \[IndentingNewLine] (*\ We\ prepend\ the\ matrix\ that\ pairs\ showing\ a\ distance\ of\ \ 0\ will\ read . \ These\ pairs\ are\ those\ that\ are\ not\ connected, \ and\ the\ pairs\ consisting\ of\ a\ node\ with\ \(\(itself\)\(.\)\ \)\ *) \[IndentingNewLine]MapIndexed[\((powersOfAdjMatrix[\([#1, Apply[Sequence, #2]]\)])\) &, distancesMatrix + Table[1, {V[g]}, {V[ g]}], {2}]\[IndentingNewLine]];\)\[IndentingNewLine]\ \[IndentingNewLine]\[IndentingNewLine] (*\ This\ function\ returns\ the\ betweeness\ of\ node\ v . \ The\ betweenness\ of\ a\ node\ v\ is\ calculated\ by\ computing, \ for\ every\ pair\ of\ other\ nodes\ s, t\ in\ the\ network\ \((s \[NotEqual] v \[NotEqual] t)\), \ the\ fraction\ of\ all\ the\ shortest\ paths\ between\ s\ and\ t\ that\ \ pass\ through\ v . \ These\ \((n\ \[Dash]\ 1)\) \((n\ \[Dash]\ 2)\)\ fractions\ are\ \ then\ summed\ up . \ The\ idea\ in\ this\ algorithm\ is\ that\ the\ number\ of\ shortest\ \ paths\ between\ s\ and\ s\ that\ do\ not\ pass\ through\ a\ node\ v\ are\ \ the\ number\ of\ paths\ between\ s\ and\ t\ OF\ LENGTH\ EQUAL\ TO\ THE\ \ DISTANCE\ BETWEEN\ s\ AND\ t\ IN\ THE\ ORIGINAL\ GRAPH, \ in\ a\ graph\ where\ node\ v\ has\ been\ \(\(deleted\)\(.\)\)\ *) \ \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(Betweenness[v_Integer, g_Graph] := Module[{distancesMatrix, adjMatrix, powersOfAdjMatrix, nShortestPaths, adjMatrixWithoutVertex, powersOfAdjMatrixWithoutVertex, nShortestPathsNotThroughV}, \ \[IndentingNewLine]\[IndentingNewLine]If[\((UndirectedQ[ g]\ && \ \(! ConnectedQ[ g]\))\)\ || \ \((\(! UndirectedQ[ g]\)\ && \ \(! ConnectedQ[g, Strong]\))\), \ \[IndentingNewLine]Print["\"]; \ Return[];\[IndentingNewLine]]; \[IndentingNewLine]\ \[IndentingNewLine]distancesMatrix\ = \ AllPairsShortestPath[ g]; \[IndentingNewLine]\[IndentingNewLine] (*\ Calculate\ the\ number\ of\ shortest\ paths\ between\ any\ two\ \ nodes\ in\ the\ graph\ *) \[IndentingNewLine]adjMatrix\ = \ ToAdjacencyMatrix[g]; \[IndentingNewLine]powersOfAdjMatrix\ = \ NestList[\((# . adjMatrix)\) &, adjMatrix, Max[distancesMatrix] - 1]; \[IndentingNewLine]PrependTo[ powersOfAdjMatrix, Table[0, {V[g]}, {V[g]}]]; (*\ We\ prepend\ the\ matrix\ that\ pairs\ showing\ a\ distance\ of\ \ 0\ will\ read . \ These\ pairs\ are\ those\ that\ are\ not\ connected, \ and\ the\ pairs\ consisting\ of\ a\ node\ with\ \(\(itself\)\(.\)\ \)\ *) \[IndentingNewLine]nShortestPaths = MapIndexed[\((powersOfAdjMatrix[\([#1, Apply[Sequence, #2]]\)])\) &, distancesMatrix + Table[1, {V[g]}, {V[ g]}], {2}]; \[IndentingNewLine]\[IndentingNewLine] (*\ Calculate\ the\ number\ of\ paths\ between\ i\ and\ j\ OF\ LENGTH\ \ EQUAL\ TO\ THE\ DISTANCE\ BETWEEN\ i\ AND\ j\ IN\ THE\ ORIGINAL\ GRAPH, \ in\ a\ graph\ where\ node\ v\ has\ been\ deleted . \ This\ is\ the\ number\ of\ shortest\ paths\ between\ i\ and\ \ j\ that\ do\ not\ pass\ through\ node\ v\ in\ the\ original\ \(\(graph\)\(.\)\ \)\ *) \[IndentingNewLine]adjMatrixWithoutVertex\ = \ Drop[adjMatrix, {v}, {v}]; \ \[IndentingNewLine]powersOfAdjMatrixWithoutVertex\ = \ NestList[\((# . adjMatrixWithoutVertex)\) &, adjMatrixWithoutVertex, Max[distancesMatrix] - 1]; \[IndentingNewLine]PrependTo[ powersOfAdjMatrixWithoutVertex, Table[0, {V[g]}, {V[g]}]]; (*\ We\ prepend\ the\ matrix\ that\ pairs\ showing\ a\ distance\ of\ \ 0\ will\ read . \ These\ pairs\ are\ those\ that\ are\ not\ connected, \ and\ the\ pairs\ consisting\ of\ a\ node\ with\ \(\(itself\)\(.\)\ \)\ *) \[IndentingNewLine]nShortestPathsNotThroughV = MapIndexed[\((powersOfAdjMatrixWithoutVertex[\([#1, Apply[Sequence, #2]]\)])\) &, Drop[distancesMatrix, {v}, {v}] + Table[1, {V[g] - 1}, {V[g] - 1}], {2}]; \[IndentingNewLine]\[IndentingNewLine] (*\ Return\ the\ betweenness\ *) \[IndentingNewLine]Total[\((Drop[ nShortestPaths, {v}, {v}] - nShortestPathsNotThroughV)\)/\((Drop[ nShortestPaths, {v}, {v}] - IdentityMatrix[V[g] - 1])\), 2]\[IndentingNewLine]];\)\[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine] (*\ This\ function\ returns\ a\ list\ with\ the\ betweeness\ of\ every\ \ node\ in\ the\ network . \ The\ betweenness\ of\ a\ node\ v\ is\ calculated\ by\ computing, \ for\ every\ pair\ of\ other\ nodes\ s, t\ in\ the\ network\ \((s \[NotEqual] v \[NotEqual] t)\), \ the\ fraction\ of\ all\ the\ shortest\ paths\ between\ s\ and\ t\ that\ \ pass\ through\ v . \ These\ \((n\ \[Dash]\ 1)\) \((n\ \[Dash]\ 2)\)\ fractions\ are\ \ then\ summed\ up . \ The\ idea\ in\ this\ algorithm\ is\ that\ the\ number\ of\ shortest\ \ paths\ between\ s\ and\ s\ that\ do\ not\ pass\ through\ a\ node\ v\ are\ \ the\ number\ of\ paths\ between\ s\ and\ t\ OF\ LENGTH\ EQUAL\ TO\ THE\ \ DISTANCE\ BETWEEN\ s\ AND\ t\ IN\ THE\ ORIGINAL\ GRAPH, \ in\ a\ graph\ where\ node\ v\ has\ been\ \(\(deleted\)\(.\)\)\ *) \ \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(Betweenness[g_Graph] := Module[{nNodes, distancesMatrix, adjMatrix, powersOfAdjMatrix, nShortestPaths, v, adjMatrixWithoutVertex, powersOfAdjMatrixWithoutVertex, nShortestPathsNotThroughV, betweennessList}, \ \[IndentingNewLine]\[IndentingNewLine]If[\((UndirectedQ[ g]\ && \ \(! ConnectedQ[ g]\))\)\ || \ \((\(! UndirectedQ[ g]\)\ && \ \(! ConnectedQ[g, Strong]\))\), \ \[IndentingNewLine]Print["\"]; \ Return[];\[IndentingNewLine]]; \[IndentingNewLine]\ \[IndentingNewLine]distancesMatrix\ = \ AllPairsShortestPath[g]; \[IndentingNewLine]nNodes = V[g]; \[IndentingNewLine]\[IndentingNewLine] (*\ Calculate\ the\ number\ of\ shortest\ paths\ between\ any\ two\ \ nodes\ in\ the\ graph\ *) \[IndentingNewLine]adjMatrix\ = \ ToAdjacencyMatrix[g]; \[IndentingNewLine]powersOfAdjMatrix\ = \ NestList[\((# . adjMatrix)\) &, adjMatrix, Max[distancesMatrix] - 1]; \[IndentingNewLine]PrependTo[ powersOfAdjMatrix, Table[0, {nNodes}, {nNodes}]]; (*\ We\ prepend\ the\ matrix\ that\ pairs\ showing\ a\ distance\ of\ \ 0\ will\ read . \ These\ pairs\ are\ those\ that\ are\ not\ connected, \ and\ the\ pairs\ consisting\ of\ a\ node\ with\ \(\(itself\)\(.\)\ \)\ *) \[IndentingNewLine]nShortestPaths = MapIndexed[\((powersOfAdjMatrix[\([#1, Apply[Sequence, #2]]\)])\) &, distancesMatrix + Table[1, {nNodes}, {nNodes}], {2}]; \[IndentingNewLine]\ \[IndentingNewLine]betweennessList = {}; \[IndentingNewLine] (*\ Calculate\ the\ number\ of\ paths\ between\ i\ and\ j\ OF\ LENGTH\ \ EQUAL\ TO\ THE\ DISTANCE\ BETWEEN\ i\ AND\ j\ IN\ THE\ ORIGINAL\ GRAPH, \ in\ a\ graph\ where\ node\ v\ has\ been\ deleted . \ This\ is\ the\ number\ of\ shortest\ paths\ between\ i\ and\ \ j\ that\ do\ not\ pass\ through\ node\ v\ in\ the\ original\ \(\(graph\)\(.\)\ \)\ *) \[IndentingNewLine]For[v = 1, v \[LessEqual] nNodes, \(v++\), \[IndentingNewLine]adjMatrixWithoutVertex\ = \ \ Drop[adjMatrix, {v}, {v}]; powersOfAdjMatrixWithoutVertex\ = \ NestList[\((# . adjMatrixWithoutVertex)\) &, adjMatrixWithoutVertex, Max[distancesMatrix] - 1]; \[IndentingNewLine]PrependTo[ powersOfAdjMatrixWithoutVertex, Table[0, {nNodes}, {nNodes}]]; (*\ We\ prepend\ the\ matrix\ that\ pairs\ showing\ a\ distance\ of\ \ 0\ will\ read . \ These\ pairs\ are\ those\ that\ are\ not\ connected, \ and\ the\ pairs\ consisting\ of\ a\ node\ with\ \(\(itself\)\(.\ \)\)\ *) \[IndentingNewLine]nShortestPathsNotThroughV = MapIndexed[\((powersOfAdjMatrixWithoutVertex[\([#1, Apply[Sequence, #2]]\)])\) &, Drop[distancesMatrix, {v}, {v}] + Table[1, {nNodes - 1}, {nNodes - 1}], {2}]; \ \[IndentingNewLine]\[IndentingNewLine]AppendTo[betweennessList, Total[\((Drop[nShortestPaths, {v}, {v}] - nShortestPathsNotThroughV)\)/\((Drop[ nShortestPaths, {v}, {v}] - IdentityMatrix[V[g] - 1])\), 2]];\[IndentingNewLine]]; \[IndentingNewLine]\ \[IndentingNewLine] (*\ Return\ the\ betweenness\ *) \[IndentingNewLine]betweennessList\ \[IndentingNewLine]];\)\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Basics Concepts and Terminology", "Section"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(myBinaryTree = CompleteBinaryTree[50];\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(g1 = ShowGraph[myBinaryTree, \ DisplayFunction \[Rule] Identity];\)\), "\n", \(\(g2 = ShowGraph[SpringEmbedding[myBinaryTree, 200, 0.05], \ DisplayFunction \[Rule] Identity];\)\), "\n", 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71336 .43506 L s 71336 .43506 m 71336 .45362 L s 75046 .43506 m 76902 .43506 L s 75046 .43506 m 75046 .45362 L s 76902 .43506 m 78757 .43506 L s 78757 .43506 m 80612 .43506 L s 78757 .43506 m 78757 .45362 L s 80612 .43506 m 82468 .43506 L s 80612 .43506 m 80612 .45362 L s 82468 .43506 m 82468 .45362 L s 86178 .43506 m 88033 .43506 L s 88033 .43506 m 89889 .43506 L s 88033 .43506 m 88033 .45362 L s 89889 .43506 m 91744 .43506 L s 89889 .43506 m 89889 .45362 L s 04545 .45362 m 04545 .47217 L s 10111 .45362 m 11967 .45362 L s 10111 .45362 m 10111 .47217 L s 11967 .45362 m 11967 .47217 L s 19388 .45362 m 19388 .47217 L s 24954 .45362 m 26809 .45362 L s 24954 .45362 m 24954 .47217 L s 26809 .45362 m 26809 .47217 L s 30519 .45362 m 32375 .45362 L s 30519 .45362 m 30519 .47217 L s 36085 .45362 m 36085 .47217 L s 47217 .45362 m 47217 .47217 L s 50928 .45362 m 52783 .45362 L s 50928 .45362 m 50928 .47217 L s 52783 .45362 m 54638 .45362 L s 52783 .45362 m 52783 .47217 L s 54638 .45362 m 56494 .45362 L s 56494 .45362 m 58349 .45362 L s 58349 .45362 m 60204 .45362 L s 58349 .45362 m 58349 .47217 L s 63915 .45362 m 6577 .45362 L s 63915 .45362 m 63915 .47217 L s 6577 .45362 m 6577 .47217 L s 71336 .45362 m 73191 .45362 L s 71336 .45362 m 71336 .47217 L s 73191 .45362 m 75046 .45362 L s 73191 .45362 m 73191 .47217 L s 75046 .45362 m 75046 .47217 L s 78757 .45362 m 80612 .45362 L s 80612 .45362 m 82468 .45362 L s 88033 .45362 m 89889 .45362 L s 93599 .45362 m 93599 .47217 L s 04545 .47217 m 06401 .47217 L s 06401 .47217 m 08256 .47217 L s 08256 .47217 m 10111 .47217 L s 08256 .47217 m 08256 .49072 L s 10111 .47217 m 11967 .47217 L s 11967 .47217 m 13822 .47217 L s 13822 .47217 m 13822 .49072 L s 24954 .47217 m 26809 .47217 L s 24954 .47217 m 24954 .49072 L s 26809 .47217 m 26809 .49072 L s 30519 .47217 m 30519 .49072 L s 3423 .47217 m 36085 .47217 L s 3423 .47217 m 3423 .49072 L s 36085 .47217 m 36085 .49072 L s 39796 .47217 m 39796 .49072 L s 45362 .47217 m 47217 .47217 L s 47217 .47217 m 47217 .49072 L s 50928 .47217 m 52783 .47217 L s 50928 .47217 m 50928 .49072 L s 63915 .47217 m 6577 .47217 L s 71336 .47217 m 73191 .47217 L s 71336 .47217 m 71336 .49072 L s 73191 .47217 m 75046 .47217 L s 73191 .47217 m 73191 .49072 L s 86178 .47217 m 86178 .49072 L s 91744 .47217 m 93599 .47217 L s 91744 .47217 m 91744 .49072 L s 93599 .47217 m 93599 .49072 L s 13822 .49072 m 13822 .50928 L s 21243 .49072 m 23098 .49072 L s 23098 .49072 m 24954 .49072 L s 24954 .49072 m 26809 .49072 L s 24954 .49072 m 24954 .50928 L s 3423 .49072 m 36085 .49072 L s 36085 .49072 m 37941 .49072 L s 36085 .49072 m 36085 .50928 L s 37941 .49072 m 39796 .49072 L s 37941 .49072 m 37941 .50928 L s 39796 .49072 m 41651 .49072 L s 47217 .49072 m 49072 .49072 L s 47217 .49072 m 47217 .50928 L s 49072 .49072 m 50928 .49072 L s 49072 .49072 m 49072 .50928 L s 71336 .49072 m 73191 .49072 L s 73191 .49072 m 73191 .50928 L s 78757 .49072 m 78757 .50928 L s 84323 .49072 m 86178 .49072 L s 86178 .49072 m 88033 .49072 L s 86178 .49072 m 86178 .50928 L s 91744 .49072 m 93599 .49072 L s 91744 .49072 m 91744 .50928 L s 93599 .49072 m 95455 .49072 L s 95455 .49072 m 95455 .50928 L s 04545 .50928 m 06401 .50928 L s 11967 .50928 m 13822 .50928 L s 11967 .50928 m 11967 .52783 L s 13822 .50928 m 15677 .50928 L s 24954 .50928 m 24954 .52783 L s 36085 .50928 m 37941 .50928 L s 36085 .50928 m 36085 .52783 L s 43506 .50928 m 43506 .52783 L s 47217 .50928 m 49072 .50928 L s 52783 .50928 m 52783 .52783 L s 56494 .50928 m 58349 .50928 L s 56494 .50928 m 56494 .52783 L s 58349 .50928 m 60204 .50928 L s 63915 .50928 m 6577 .50928 L s 63915 .50928 m 63915 .52783 L s 6577 .50928 m 67625 .50928 L s 6577 .50928 m 6577 .52783 L s 67625 .50928 m 67625 .52783 L s 73191 .50928 m 73191 .52783 L s 76902 .50928 m 78757 .50928 L s 76902 .50928 m 76902 .52783 L s 86178 .50928 m 86178 .52783 L s 95455 .50928 m 95455 .52783 L s 11967 .52783 m 11967 .54638 L s 19388 .52783 m 19388 .54638 L s 24954 .52783 m 24954 .54638 L s 30519 .52783 m 32375 .52783 L s 32375 .52783 m 3423 .52783 L s 32375 .52783 m 32375 .54638 L s 3423 .52783 m 36085 .52783 L s 3423 .52783 m 3423 .54638 L s 36085 .52783 m 36085 .54638 L s 39796 .52783 m 39796 .54638 L s 52783 .52783 m 54638 .52783 L s 54638 .52783 m 56494 .52783 L s 56494 .52783 m 56494 .54638 L s 62059 .52783 m 63915 .52783 L s 63915 .52783 m 6577 .52783 L s 63915 .52783 m 63915 .54638 L s 6577 .52783 m 67625 .52783 L s 6577 .52783 m 6577 .54638 L s 67625 .52783 m 67625 .54638 L s 71336 .52783 m 73191 .52783 L s 76902 .52783 m 76902 .54638 L s 84323 .52783 m 86178 .52783 L s 84323 .52783 m 84323 .54638 L s 86178 .52783 m 88033 .52783 L s 86178 .52783 m 86178 .54638 L s 88033 .52783 m 89889 .52783 L s 88033 .52783 m 88033 .54638 L s 08256 .54638 m 10111 .54638 L s 10111 .54638 m 11967 .54638 L s 11967 .54638 m 11967 .56494 L s 19388 .54638 m 19388 .56494 L s 23098 .54638 m 24954 .54638 L s 23098 .54638 m 23098 .56494 L s 24954 .54638 m 26809 .54638 L s 26809 .54638 m 28664 .54638 L s 28664 .54638 m 28664 .56494 L s 32375 .54638 m 3423 .54638 L s 32375 .54638 m 32375 .56494 L s 3423 .54638 m 36085 .54638 L s 3423 .54638 m 3423 .56494 L s 45362 .54638 m 47217 .54638 L s 45362 .54638 m 45362 .56494 L s 47217 .54638 m 47217 .56494 L s 63915 .54638 m 6577 .54638 L s 6577 .54638 m 67625 .54638 L s 6577 .54638 m 6577 .56494 L s 67625 .54638 m 69481 .54638 L s 69481 .54638 m 69481 .56494 L s 76902 .54638 m 78757 .54638 L s 78757 .54638 m 78757 .56494 L s 84323 .54638 m 86178 .54638 L s 86178 .54638 m 88033 .54638 L s 86178 .54638 m 86178 .56494 L s 88033 .54638 m 88033 .56494 L s 91744 .54638 m 91744 .56494 L s 11967 .56494 m 13822 .56494 L s 11967 .56494 m 11967 .58349 L s 13822 .56494 m 13822 .58349 L s 17532 .56494 m 19388 .56494 L s 23098 .56494 m 23098 .58349 L s 28664 .56494 m 28664 .58349 L s 32375 .56494 m 3423 .56494 L s 32375 .56494 m 32375 .58349 L s 3423 .56494 m 3423 .58349 L s 41651 .56494 m 41651 .58349 L s 45362 .56494 m 47217 .56494 L s 45362 .56494 m 45362 .58349 L s 47217 .56494 m 49072 .56494 L s 47217 .56494 m 47217 .58349 L s 58349 .56494 m 58349 .58349 L s 62059 .56494 m 62059 .58349 L s 6577 .56494 m 6577 .58349 L s 69481 .56494 m 69481 .58349 L s 73191 .56494 m 75046 .56494 L s 73191 .56494 m 73191 .58349 L s 75046 .56494 m 75046 .58349 L s 78757 .56494 m 80612 .56494 L s 86178 .56494 m 88033 .56494 L s 88033 .56494 m 88033 .58349 L s 91744 .56494 m 93599 .56494 L s 10111 .58349 m 11967 .58349 L s 11967 .58349 m 13822 .58349 L s 13822 .58349 m 15677 .58349 L s 15677 .58349 m 15677 .60204 L s 21243 .58349 m 23098 .58349 L s 21243 .58349 m 21243 .60204 L s 26809 .58349 m 28664 .58349 L s 28664 .58349 m 30519 .58349 L s 30519 .58349 m 32375 .58349 L s 32375 .58349 m 3423 .58349 L s 32375 .58349 m 32375 .60204 L s 45362 .58349 m 47217 .58349 L s 47217 .58349 m 47217 .60204 L s 50928 .58349 m 52783 .58349 L s 52783 .58349 m 52783 .60204 L s 56494 .58349 m 58349 .58349 L s 58349 .58349 m 60204 .58349 L s 58349 .58349 m 58349 .60204 L s 60204 .58349 m 62059 .58349 L s 62059 .58349 m 63915 .58349 L s 62059 .58349 m 62059 .60204 L s 63915 .58349 m 6577 .58349 L s 6577 .58349 m 6577 .60204 L s 69481 .58349 m 71336 .58349 L s 71336 .58349 m 73191 .58349 L s 71336 .58349 m 71336 .60204 L s 73191 .58349 m 75046 .58349 L s 75046 .58349 m 75046 .60204 L s 82468 .58349 m 84323 .58349 L s 82468 .58349 m 82468 .60204 L s 84323 .58349 m 84323 .60204 L s 88033 .58349 m 88033 .60204 L s 08256 .60204 m 08256 .62059 L s 32375 .60204 m 32375 .62059 L s 47217 .60204 m 47217 .62059 L s 52783 .60204 m 54638 .60204 L s 52783 .60204 m 52783 .62059 L s 6577 .60204 m 6577 .62059 L s 75046 .60204 m 76902 .60204 L s 75046 .60204 m 75046 .62059 L s 76902 .60204 m 76902 .62059 L s 80612 .60204 m 82468 .60204 L s 80612 .60204 m 80612 .62059 L s 82468 .60204 m 84323 .60204 L s 82468 .60204 m 82468 .62059 L s 84323 .60204 m 86178 .60204 L s 84323 .60204 m 84323 .62059 L s 86178 .60204 m 88033 .60204 L s 86178 .60204 m 86178 .62059 L s 88033 .60204 m 89889 .60204 L s 93599 .60204 m 95455 .60204 L s 93599 .60204 m 93599 .62059 L s 95455 .60204 m 95455 .62059 L s 04545 .62059 m 06401 .62059 L s 04545 .62059 m 04545 .63915 L s 06401 .62059 m 08256 .62059 L s 08256 .62059 m 10111 .62059 L s 10111 .62059 m 11967 .62059 L s 11967 .62059 m 11967 .63915 L s 26809 .62059 m 28664 .62059 L s 26809 .62059 m 26809 .63915 L s 28664 .62059 m 30519 .62059 L s 30519 .62059 m 32375 .62059 L s 30519 .62059 m 30519 .63915 L s 32375 .62059 m 3423 .62059 L s 45362 .62059 m 47217 .62059 L s 47217 .62059 m 49072 .62059 L s 47217 .62059 m 47217 .63915 L s 52783 .62059 m 52783 .63915 L s 6577 .62059 m 67625 .62059 L s 6577 .62059 m 6577 .63915 L s 67625 .62059 m 69481 .62059 L s 69481 .62059 m 69481 .63915 L s 75046 .62059 m 76902 .62059 L s 76902 .62059 m 78757 .62059 L s 78757 .62059 m 80612 .62059 L s 78757 .62059 m 78757 .63915 L s 80612 .62059 m 82468 .62059 L s 80612 .62059 m 80612 .63915 L s 82468 .62059 m 84323 .62059 L s 82468 .62059 m 82468 .63915 L s 84323 .62059 m 86178 .62059 L s 84323 .62059 m 84323 .63915 L s 86178 .62059 m 86178 .63915 L s 93599 .62059 m 95455 .62059 L s 93599 .62059 m 93599 .63915 L s 95455 .62059 m 95455 .63915 L s 04545 .63915 m 04545 .6577 L s 17532 .63915 m 17532 .6577 L s 21243 .63915 m 21243 .6577 L s 30519 .63915 m 30519 .6577 L s 52783 .63915 m 52783 .6577 L s 62059 .63915 m 63915 .63915 L s 62059 .63915 m 62059 .6577 L s 63915 .63915 m 6577 .63915 L s 63915 .63915 m 63915 .6577 L s 6577 .63915 m 6577 .6577 L s 69481 .63915 m 71336 .63915 L s 69481 .63915 m 69481 .6577 L s 78757 .63915 m 80612 .63915 L s 80612 .63915 m 82468 .63915 L s 82468 .63915 m 84323 .63915 L s 84323 .63915 m 86178 .63915 L s 86178 .63915 m 88033 .63915 L s 86178 .63915 m 86178 .6577 L s 88033 .63915 m 89889 .63915 L s 89889 .63915 m 91744 .63915 L s 89889 .63915 m 89889 .6577 L s 91744 .63915 m 93599 .63915 L s 91744 .63915 m 91744 .6577 L s 93599 .63915 m 95455 .63915 L s 95455 .63915 m 95455 .6577 L s 15677 .6577 m 17532 .6577 L s 15677 .6577 m 15677 .67625 L s 17532 .6577 m 19388 .6577 L s 17532 .6577 m 17532 .67625 L s 19388 .6577 m 21243 .6577 L s 24954 .6577 m 24954 .67625 L s 30519 .6577 m 30519 .67625 L s 3423 .6577 m 36085 .6577 L s 3423 .6577 m 3423 .67625 L s 36085 .6577 m 37941 .6577 L s 36085 .6577 m 36085 .67625 L s 37941 .6577 m 37941 .67625 L s 41651 .6577 m 43506 .6577 L s 41651 .6577 m 41651 .67625 L s 43506 .6577 m 45362 .6577 L s 43506 .6577 m 43506 .67625 L s 49072 .6577 m 49072 .67625 L s 52783 .6577 m 54638 .6577 L s 54638 .6577 m 54638 .67625 L s 58349 .6577 m 60204 .6577 L s 58349 .6577 m 58349 .67625 L s 60204 .6577 m 62059 .6577 L s 60204 .6577 m 60204 .67625 L s 62059 .6577 m 63915 .6577 L s 62059 .6577 m 62059 .67625 L s 63915 .6577 m 6577 .6577 L s 6577 .6577 m 67625 .6577 L s 6577 .6577 m 6577 .67625 L s 67625 .6577 m 69481 .6577 L s 75046 .6577 m 76902 .6577 L s 75046 .6577 m 75046 .67625 L s 89889 .6577 m 91744 .6577 L s 89889 .6577 m 89889 .67625 L s 06401 .67625 m 06401 .69481 L s 13822 .67625 m 15677 .67625 L s 13822 .67625 m 13822 .69481 L s 15677 .67625 m 17532 .67625 L s 24954 .67625 m 26809 .67625 L s 30519 .67625 m 32375 .67625 L s 30519 .67625 m 30519 .69481 L s 32375 .67625 m 3423 .67625 L s 3423 .67625 m 36085 .67625 L s 3423 .67625 m 3423 .69481 L s 36085 .67625 m 37941 .67625 L s 37941 .67625 m 39796 .67625 L s 37941 .67625 m 37941 .69481 L s 39796 .67625 m 41651 .67625 L s 41651 .67625 m 43506 .67625 L s 49072 .67625 m 50928 .67625 L s 50928 .67625 m 50928 .69481 L s 58349 .67625 m 60204 .67625 L s 58349 .67625 m 58349 .69481 L s 60204 .67625 m 62059 .67625 L s 60204 .67625 m 60204 .69481 L s 62059 .67625 m 62059 .69481 L s 78757 .67625 m 78757 .69481 L s 82468 .67625 m 84323 .67625 L s 82468 .67625 m 82468 .69481 L s 84323 .67625 m 84323 .69481 L s 88033 .67625 m 89889 .67625 L s 06401 .69481 m 06401 .71336 L s 21243 .69481 m 23098 .69481 L s 23098 .69481 m 23098 .71336 L s 37941 .69481 m 37941 .71336 L s 45362 .69481 m 45362 .71336 L s 50928 .69481 m 50928 .71336 L s 56494 .69481 m 58349 .69481 L s 56494 .69481 m 56494 .71336 L s 58349 .69481 m 60204 .69481 L s 58349 .69481 m 58349 .71336 L s 60204 .69481 m 62059 .69481 L s 76902 .69481 m 78757 .69481 L s 76902 .69481 m 76902 .71336 L s 82468 .69481 m 84323 .69481 L s 82468 .69481 m 82468 .71336 L s 91744 .69481 m 93599 .69481 L s 93599 .69481 m 93599 .71336 L s 15677 .71336 m 15677 .73191 L s 19388 .71336 m 19388 .73191 L s 23098 .71336 m 24954 .71336 L s 37941 .71336 m 39796 .71336 L s 37941 .71336 m 37941 .73191 L s 39796 .71336 m 39796 .73191 L s 45362 .71336 m 45362 .73191 L s 49072 .71336 m 50928 .71336 L s 50928 .71336 m 52783 .71336 L s 50928 .71336 m 50928 .73191 L s 52783 .71336 m 54638 .71336 L s 54638 .71336 m 56494 .71336 L s 54638 .71336 m 54638 .73191 L s 56494 .71336 m 58349 .71336 L s 56494 .71336 m 56494 .73191 L s 58349 .71336 m 58349 .73191 L s 63915 .71336 m 63915 .73191 L s 75046 .71336 m 76902 .71336 L s 86178 .71336 m 88033 .71336 L s 86178 .71336 m 86178 .73191 L s 88033 .71336 m 89889 .71336 L s 89889 .71336 m 89889 .73191 L s 93599 .71336 m 93599 .73191 L s 04545 .73191 m 04545 .75046 L s 13822 .73191 m 15677 .73191 L s 13822 .73191 m 13822 .75046 L s 15677 .73191 m 17532 .73191 L s 15677 .73191 m 15677 .75046 L s 17532 .73191 m 19388 .73191 L s 17532 .73191 m 17532 .75046 L s 19388 .73191 m 19388 .75046 L s 30519 .73191 m 30519 .75046 L s 3423 .73191 m 3423 .75046 L s 37941 .73191 m 39796 .73191 L s 37941 .73191 m 37941 .75046 L s 43506 .73191 m 45362 .73191 L s 45362 .73191 m 47217 .73191 L s 54638 .73191 m 56494 .73191 L s 56494 .73191 m 58349 .73191 L s 58349 .73191 m 58349 .75046 L s 63915 .73191 m 6577 .73191 L s 63915 .73191 m 63915 .75046 L s 71336 .73191 m 71336 .75046 L s 89889 .73191 m 91744 .73191 L s 91744 .73191 m 93599 .73191 L s 93599 .73191 m 93599 .75046 L s 08256 .75046 m 10111 .75046 L s 10111 .75046 m 10111 .76902 L s 13822 .75046 m 15677 .75046 L s 13822 .75046 m 13822 .76902 L s 15677 .75046 m 17532 .75046 L s 17532 .75046 m 19388 .75046 L s 17532 .75046 m 17532 .76902 L s 19388 .75046 m 21243 .75046 L s 19388 .75046 m 19388 .76902 L s 21243 .75046 m 21243 .76902 L s 24954 .75046 m 24954 .76902 L s 28664 .75046 m 30519 .75046 L s 28664 .75046 m 28664 .76902 L s 30519 .75046 m 32375 .75046 L s 30519 .75046 m 30519 .76902 L s 32375 .75046 m 3423 .75046 L s 32375 .75046 m 32375 .76902 L s 3423 .75046 m 3423 .76902 L s 41651 .75046 m 41651 .76902 L s 49072 .75046 m 49072 .76902 L s 52783 .75046 m 52783 .76902 L s 58349 .75046 m 58349 .76902 L s 62059 .75046 m 63915 .75046 L s 62059 .75046 m 62059 .76902 L s 63915 .75046 m 63915 .76902 L s 69481 .75046 m 71336 .75046 L s 71336 .75046 m 73191 .75046 L s 71336 .75046 m 71336 .76902 L s 76902 .75046 m 78757 .75046 L s 78757 .75046 m 78757 .76902 L s 93599 .75046 m 93599 .76902 L s 10111 .76902 m 10111 .78757 L s 17532 .76902 m 19388 .76902 L s 19388 .76902 m 21243 .76902 L s 21243 .76902 m 21243 .78757 L s 28664 .76902 m 30519 .76902 L s 28664 .76902 m 28664 .78757 L s 30519 .76902 m 32375 .76902 L s 30519 .76902 m 30519 .78757 L s 32375 .76902 m 3423 .76902 L s 32375 .76902 m 32375 .78757 L s 3423 .76902 m 36085 .76902 L s 3423 .76902 m 3423 .78757 L s 36085 .76902 m 36085 .78757 L s 41651 .76902 m 43506 .76902 L s 43506 .76902 m 43506 .78757 L s 52783 .76902 m 52783 .78757 L s 56494 .76902 m 58349 .76902 L s 58349 .76902 m 60204 .76902 L s 58349 .76902 m 58349 .78757 L s 60204 .76902 m 62059 .76902 L s 62059 .76902 m 63915 .76902 L s 63915 .76902 m 63915 .78757 L s 78757 .76902 m 80612 .76902 L s 80612 .76902 m 82468 .76902 L s 82468 .76902 m 84323 .76902 L s 82468 .76902 m 82468 .78757 L s 84323 .76902 m 86178 .76902 L s 86178 .76902 m 86178 .78757 L s 04545 .78757 m 06401 .78757 L s 04545 .78757 m 04545 .80612 L s 06401 .78757 m 08256 .78757 L s 06401 .78757 m 06401 .80612 L s 08256 .78757 m 10111 .78757 L s 08256 .78757 m 08256 .80612 L s 21243 .78757 m 21243 .80612 L s 26809 .78757 m 28664 .78757 L s 28664 .78757 m 30519 .78757 L s 28664 .78757 m 28664 .80612 L s 30519 .78757 m 32375 .78757 L s 32375 .78757 m 3423 .78757 L s 32375 .78757 m 32375 .80612 L s 3423 .78757 m 36085 .78757 L s 36085 .78757 m 36085 .80612 L s 63915 .78757 m 6577 .78757 L s 6577 .78757 m 6577 .80612 L s 82468 .78757 m 82468 .80612 L s 86178 .78757 m 86178 .80612 L s 04545 .80612 m 06401 .80612 L s 06401 .80612 m 08256 .80612 L s 08256 .80612 m 08256 .82468 L s 13822 .80612 m 13822 .82468 L s 19388 .80612 m 21243 .80612 L s 19388 .80612 m 19388 .82468 L s 28664 .80612 m 28664 .82468 L s 36085 .80612 m 37941 .80612 L s 37941 .80612 m 39796 .80612 L s 39796 .80612 m 39796 .82468 L s 47217 .80612 m 49072 .80612 L s 47217 .80612 m 47217 .82468 L s 6577 .80612 m 6577 .82468 L s 76902 .80612 m 76902 .82468 L s 86178 .80612 m 88033 .80612 L s 88033 .80612 m 89889 .80612 L s 88033 .80612 m 88033 .82468 L s 08256 .82468 m 08256 .84323 L s 24954 .82468 m 26809 .82468 L s 24954 .82468 m 24954 .84323 L s 26809 .82468 m 28664 .82468 L s 28664 .82468 m 30519 .82468 L s 28664 .82468 m 28664 .84323 L s 30519 .82468 m 30519 .84323 L s 39796 .82468 m 41651 .82468 L s 39796 .82468 m 39796 .84323 L s 41651 .82468 m 41651 .84323 L s 45362 .82468 m 47217 .82468 L s 45362 .82468 m 45362 .84323 L s 47217 .82468 m 47217 .84323 L s 58349 .82468 m 60204 .82468 L s 60204 .82468 m 62059 .82468 L s 60204 .82468 m 60204 .84323 L s 62059 .82468 m 63915 .82468 L s 63915 .82468 m 6577 .82468 L s 76902 .82468 m 76902 .84323 L s 91744 .82468 m 93599 .82468 L s 93599 .82468 m 95455 .82468 L s 95455 .82468 m 95455 .84323 L s 04545 .84323 m 06401 .84323 L s 04545 .84323 m 04545 .86178 L s 06401 .84323 m 08256 .84323 L s 08256 .84323 m 08256 .86178 L s 28664 .84323 m 30519 .84323 L s 30519 .84323 m 32375 .84323 L s 32375 .84323 m 32375 .86178 L s 39796 .84323 m 41651 .84323 L s 39796 .84323 m 39796 .86178 L s 41651 .84323 m 41651 .86178 L s 45362 .84323 m 47217 .84323 L s 47217 .84323 m 49072 .84323 L s 84323 .84323 m 86178 .84323 L s 84323 .84323 m 84323 .86178 L s 11967 .86178 m 11967 .88033 L s 32375 .86178 m 3423 .86178 L s 32375 .86178 m 32375 .88033 L s 3423 .86178 m 36085 .86178 L s 36085 .86178 m 36085 .88033 L s 39796 .86178 m 41651 .86178 L s 41651 .86178 m 41651 .88033 L s 56494 .86178 m 58349 .86178 L s 56494 .86178 m 56494 .88033 L s 58349 .86178 m 58349 .88033 L s 67625 .86178 m 69481 .86178 L s 67625 .86178 m 67625 .88033 L s 69481 .86178 m 71336 .86178 L s 69481 .86178 m 69481 .88033 L s 82468 .86178 m 84323 .86178 L s 82468 .86178 m 82468 .88033 L s 84323 .86178 m 84323 .88033 L s 89889 .86178 m 91744 .86178 L s 89889 .86178 m 89889 .88033 L s 91744 .86178 m 93599 .86178 L s 91744 .86178 m 91744 .88033 L s 93599 .86178 m 93599 .88033 L s 10111 .88033 m 11967 .88033 L s 10111 .88033 m 10111 .89889 L s 11967 .88033 m 11967 .89889 L s 19388 .88033 m 19388 .89889 L s 23098 .88033 m 23098 .89889 L s 26809 .88033 m 26809 .89889 L s 32375 .88033 m 32375 .89889 L s 36085 .88033 m 36085 .89889 L s 41651 .88033 m 43506 .88033 L s 41651 .88033 m 41651 .89889 L s 43506 .88033 m 45362 .88033 L s 43506 .88033 m 43506 .89889 L s 56494 .88033 m 58349 .88033 L s 62059 .88033 m 62059 .89889 L s 6577 .88033 m 67625 .88033 L s 67625 .88033 m 69481 .88033 L s 73191 .88033 m 73191 .89889 L s 76902 .88033 m 76902 .89889 L s 82468 .88033 m 84323 .88033 L s 84323 .88033 m 86178 .88033 L s 86178 .88033 m 88033 .88033 L s 88033 .88033 m 89889 .88033 L s 88033 .88033 m 88033 .89889 L s 89889 .88033 m 91744 .88033 L s 91744 .88033 m 93599 .88033 L s 93599 .88033 m 95455 .88033 L s 04545 .89889 m 06401 .89889 L s 04545 .89889 m 04545 .91744 L s 06401 .89889 m 08256 .89889 L s 06401 .89889 m 06401 .91744 L s 08256 .89889 m 10111 .89889 L s 10111 .89889 m 11967 .89889 L s 10111 .89889 m 10111 .91744 L s 11967 .89889 m 13822 .89889 L s 11967 .89889 m 11967 .91744 L s 13822 .89889 m 15677 .89889 L s 15677 .89889 m 15677 .91744 L s 19388 .89889 m 19388 .91744 L s 23098 .89889 m 23098 .91744 L s 26809 .89889 m 28664 .89889 L s 28664 .89889 m 28664 .91744 L s 32375 .89889 m 32375 .91744 L s 36085 .89889 m 36085 .91744 L s 41651 .89889 m 43506 .89889 L s 43506 .89889 m 43506 .91744 L s 62059 .89889 m 63915 .89889 L s 62059 .89889 m 62059 .91744 L s 63915 .89889 m 63915 .91744 L s 73191 .89889 m 75046 .89889 L s 73191 .89889 m 73191 .91744 L s 75046 .89889 m 76902 .89889 L s 76902 .89889 m 76902 .91744 L s 04545 .91744 m 06401 .91744 L s 06401 .91744 m 06401 .93599 L s 10111 .91744 m 11967 .91744 L s 19388 .91744 m 21243 .91744 L s 19388 .91744 m 19388 .93599 L s 21243 .91744 m 23098 .91744 L s 23098 .91744 m 24954 .91744 L s 23098 .91744 m 23098 .93599 L s 24954 .91744 m 24954 .93599 L s 28664 .91744 m 30519 .91744 L s 28664 .91744 m 28664 .93599 L s 30519 .91744 m 32375 .91744 L s 30519 .91744 m 30519 .93599 L s 32375 .91744 m 3423 .91744 L s 3423 .91744 m 36085 .91744 L s 3423 .91744 m 3423 .93599 L s 43506 .91744 m 45362 .91744 L s 56494 .91744 m 58349 .91744 L s 62059 .91744 m 63915 .91744 L s 62059 .91744 m 62059 .93599 L s 63915 .91744 m 63915 .93599 L s 73191 .91744 m 73191 .93599 L s 76902 .91744 m 78757 .91744 L s 78757 .91744 m 78757 .93599 L s 82468 .91744 m 82468 .93599 L s 86178 .91744 m 86178 .93599 L s 89889 .91744 m 91744 .91744 L s 89889 .91744 m 89889 .93599 L s 91744 .91744 m 91744 .93599 L s 06401 .93599 m 08256 .93599 L s 06401 .93599 m 06401 .95455 L s 17532 .93599 m 19388 .93599 L s 17532 .93599 m 17532 .95455 L s 23098 .93599 m 24954 .93599 L s 23098 .93599 m 23098 .95455 L s 28664 .93599 m 30519 .93599 L s 28664 .93599 m 28664 .95455 L s 30519 .93599 m 30519 .95455 L s 37941 .93599 m 37941 .95455 L s 60204 .93599 m 62059 .93599 L s 60204 .93599 m 60204 .95455 L s 62059 .93599 m 63915 .93599 L s 62059 .93599 m 62059 .95455 L s 63915 .93599 m 6577 .93599 L s 63915 .93599 m 63915 .95455 L s 6577 .93599 m 6577 .95455 L s 71336 .93599 m 73191 .93599 L s 71336 .93599 m 71336 .95455 L s 73191 .93599 m 73191 .95455 L s 78757 .93599 m 78757 .95455 L s 82468 .93599 m 84323 .93599 L s 82468 .93599 m 82468 .95455 L s 84323 .93599 m 86178 .93599 L s 84323 .93599 m 84323 .95455 L s 86178 .93599 m 86178 .95455 L s 89889 .93599 m 91744 .93599 L s 89889 .93599 m 89889 .95455 L s 10111 .95455 m 11967 .95455 L s 21243 .95455 m 23098 .95455 L s 28664 .95455 m 30519 .95455 L s 36085 .95455 m 37941 .95455 L s 41651 .95455 m 43506 .95455 L s 43506 .95455 m 45362 .95455 L s 45362 .95455 m 47217 .95455 L s 47217 .95455 m 49072 .95455 L s 54638 .95455 m 56494 .95455 L s 56494 .95455 m 58349 .95455 L s 58349 .95455 m 60204 .95455 L s 60204 .95455 m 62059 .95455 L s 62059 .95455 m 63915 .95455 L s 63915 .95455 m 6577 .95455 L s 6577 .95455 m 67625 .95455 L s 71336 .95455 m 73191 .95455 L s 73191 .95455 m 75046 .95455 L s 78757 .95455 m 80612 .95455 L s 80612 .95455 m 82468 .95455 L s 82468 .95455 m 84323 .95455 L s 84323 .95455 m 86178 .95455 L s 86178 .95455 m 88033 .95455 L s 88033 .95455 m 89889 .95455 L s 0 w 04545 .04545 Mdot 11967 .04545 Mdot 15677 .04545 Mdot 19388 .04545 Mdot 21243 .04545 Mdot 23098 .04545 Mdot 24954 .04545 Mdot 28664 .04545 Mdot 32375 .04545 Mdot 3423 .04545 Mdot 36085 .04545 Mdot 37941 .04545 Mdot 56494 .04545 Mdot 69481 .04545 Mdot 71336 .04545 Mdot 73191 .04545 Mdot 75046 .04545 Mdot 76902 .04545 Mdot 78757 .04545 Mdot 82468 .04545 Mdot 88033 .04545 Mdot 93599 .04545 Mdot 04545 .06401 Mdot 06401 .06401 Mdot 10111 .06401 Mdot 15677 .06401 Mdot 21243 .06401 Mdot 23098 .06401 Mdot 24954 .06401 Mdot 28664 .06401 Mdot 3423 .06401 Mdot 37941 .06401 Mdot 41651 .06401 Mdot 43506 .06401 Mdot 58349 .06401 Mdot 62059 .06401 Mdot 67625 .06401 Mdot 69481 .06401 Mdot 80612 .06401 Mdot 82468 .06401 Mdot 84323 .06401 Mdot 88033 .06401 Mdot 04545 .08256 Mdot 10111 .08256 Mdot 11967 .08256 Mdot 13822 .08256 Mdot 19388 .08256 Mdot 21243 .08256 Mdot 23098 .08256 Mdot 24954 .08256 Mdot 30519 .08256 Mdot 39796 .08256 Mdot 45362 .08256 Mdot 47217 .08256 Mdot 54638 .08256 Mdot 58349 .08256 Mdot 63915 .08256 Mdot 6577 .08256 Mdot 69481 .08256 Mdot 84323 .08256 Mdot 86178 .08256 Mdot 91744 .08256 Mdot 93599 .08256 Mdot 95455 .08256 Mdot 04545 .10111 Mdot 06401 .10111 Mdot 08256 .10111 Mdot 19388 .10111 Mdot 21243 .10111 Mdot 23098 .10111 Mdot 26809 .10111 Mdot 30519 .10111 Mdot 32375 .10111 Mdot 37941 .10111 Mdot 39796 .10111 Mdot 43506 .10111 Mdot 45362 .10111 Mdot 50928 .10111 Mdot 56494 .10111 Mdot 58349 .10111 Mdot 73191 .10111 Mdot 78757 .10111 Mdot 80612 .10111 Mdot 82468 .10111 Mdot 89889 .10111 Mdot 93599 .10111 Mdot 95455 .10111 Mdot 04545 .11967 Mdot 11967 .11967 Mdot 15677 .11967 Mdot 21243 .11967 Mdot 24954 .11967 Mdot 26809 .11967 Mdot 28664 .11967 Mdot 30519 .11967 Mdot 3423 .11967 Mdot 36085 .11967 Mdot 41651 .11967 Mdot 47217 .11967 Mdot 50928 .11967 Mdot 56494 .11967 Mdot 58349 .11967 Mdot 63915 .11967 Mdot 69481 .11967 Mdot 75046 .11967 Mdot 80612 .11967 Mdot 82468 .11967 Mdot 86178 .11967 Mdot 89889 .11967 Mdot 04545 .13822 Mdot 11967 .13822 Mdot 19388 .13822 Mdot 28664 .13822 Mdot 36085 .13822 Mdot 39796 .13822 Mdot 43506 .13822 Mdot 45362 .13822 Mdot 49072 .13822 Mdot 50928 .13822 Mdot 52783 .13822 Mdot 56494 .13822 Mdot 60204 .13822 Mdot 62059 .13822 Mdot 67625 .13822 Mdot 75046 .13822 Mdot 76902 .13822 Mdot 82468 .13822 Mdot 91744 .13822 Mdot 93599 .13822 Mdot 95455 .13822 Mdot 11967 .15677 Mdot 15677 .15677 Mdot 21243 .15677 Mdot 24954 .15677 Mdot 28664 .15677 Mdot 30519 .15677 Mdot 37941 .15677 Mdot 39796 .15677 Mdot 41651 .15677 Mdot 49072 .15677 Mdot 50928 .15677 Mdot 54638 .15677 Mdot 56494 .15677 Mdot 60204 .15677 Mdot 62059 .15677 Mdot 63915 .15677 Mdot 69481 .15677 Mdot 73191 .15677 Mdot 75046 .15677 Mdot 76902 .15677 Mdot 80612 .15677 Mdot 86178 .15677 Mdot 88033 .15677 Mdot 89889 .15677 Mdot 93599 .15677 Mdot 04545 .17532 Mdot 08256 .17532 Mdot 15677 .17532 Mdot 21243 .17532 Mdot 26809 .17532 Mdot 30519 .17532 Mdot 41651 .17532 Mdot 47217 .17532 Mdot 49072 .17532 Mdot 52783 .17532 Mdot 56494 .17532 Mdot 62059 .17532 Mdot 69481 .17532 Mdot 71336 .17532 Mdot 73191 .17532 Mdot 76902 .17532 Mdot 78757 .17532 Mdot 84323 .17532 Mdot 88033 .17532 Mdot 89889 .17532 Mdot 93599 .17532 Mdot 04545 .19388 Mdot 06401 .19388 Mdot 08256 .19388 Mdot 10111 .19388 Mdot 11967 .19388 Mdot 17532 .19388 Mdot 26809 .19388 Mdot 30519 .19388 Mdot 32375 .19388 Mdot 3423 .19388 Mdot 45362 .19388 Mdot 47217 .19388 Mdot 50928 .19388 Mdot 6577 .19388 Mdot 67625 .19388 Mdot 75046 .19388 Mdot 78757 .19388 Mdot 84323 .19388 Mdot 86178 .19388 Mdot 88033 .19388 Mdot 93599 .19388 Mdot 06401 .21243 Mdot 08256 .21243 Mdot 11967 .21243 Mdot 19388 .21243 Mdot 21243 .21243 Mdot 23098 .21243 Mdot 24954 .21243 Mdot 28664 .21243 Mdot 30519 .21243 Mdot 3423 .21243 Mdot 39796 .21243 Mdot 41651 .21243 Mdot 47217 .21243 Mdot 50928 .21243 Mdot 52783 .21243 Mdot 54638 .21243 Mdot 56494 .21243 Mdot 60204 .21243 Mdot 62059 .21243 Mdot 63915 .21243 Mdot 6577 .21243 Mdot 67625 .21243 Mdot 71336 .21243 Mdot 75046 .21243 Mdot 78757 .21243 Mdot 80612 .21243 Mdot 82468 .21243 Mdot 86178 .21243 Mdot 88033 .21243 Mdot 91744 .21243 Mdot 95455 .21243 Mdot 04545 .23098 Mdot 13822 .23098 Mdot 21243 .23098 Mdot 23098 .23098 Mdot 24954 .23098 Mdot 26809 .23098 Mdot 30519 .23098 Mdot 37941 .23098 Mdot 39796 .23098 Mdot 43506 .23098 Mdot 58349 .23098 Mdot 62059 .23098 Mdot 63915 .23098 Mdot 6577 .23098 Mdot 67625 .23098 Mdot 69481 .23098 Mdot 76902 .23098 Mdot 78757 .23098 Mdot 93599 .23098 Mdot 04545 .24954 Mdot 10111 .24954 Mdot 11967 .24954 Mdot 13822 .24954 Mdot 15677 .24954 Mdot 26809 .24954 Mdot 28664 .24954 Mdot 30519 .24954 Mdot 32375 .24954 Mdot 3423 .24954 Mdot 36085 .24954 Mdot 37941 .24954 Mdot 54638 .24954 Mdot 56494 .24954 Mdot 62059 .24954 Mdot 63915 .24954 Mdot 67625 .24954 Mdot 73191 .24954 Mdot 75046 .24954 Mdot 76902 .24954 Mdot 82468 .24954 Mdot 88033 .24954 Mdot 95455 .24954 Mdot 08256 .26809 Mdot 17532 .26809 Mdot 23098 .26809 Mdot 28664 .26809 Mdot 30519 .26809 Mdot 3423 .26809 Mdot 37941 .26809 Mdot 41651 .26809 Mdot 49072 .26809 Mdot 50928 .26809 Mdot 58349 .26809 Mdot 60204 .26809 Mdot 62059 .26809 Mdot 63915 .26809 Mdot 6577 .26809 Mdot 71336 .26809 Mdot 75046 .26809 Mdot 76902 .26809 Mdot 80612 .26809 Mdot 88033 .26809 Mdot 89889 .26809 Mdot 11967 .28664 Mdot 13822 .28664 Mdot 15677 .28664 Mdot 21243 .28664 Mdot 26809 .28664 Mdot 28664 .28664 Mdot 30519 .28664 Mdot 32375 .28664 Mdot 3423 .28664 Mdot 36085 .28664 Mdot 37941 .28664 Mdot 39796 .28664 Mdot 41651 .28664 Mdot 43506 .28664 Mdot 50928 .28664 Mdot 52783 .28664 Mdot 54638 .28664 Mdot 56494 .28664 Mdot 58349 .28664 Mdot 60204 .28664 Mdot 63915 .28664 Mdot 76902 .28664 Mdot 88033 .28664 Mdot 89889 .28664 Mdot 91744 .28664 Mdot 04545 .30519 Mdot 06401 .30519 Mdot 08256 .30519 Mdot 10111 .30519 Mdot 15677 .30519 Mdot 17532 .30519 Mdot 19388 .30519 Mdot 24954 .30519 Mdot 26809 .30519 Mdot 28664 .30519 Mdot 30519 .30519 Mdot 3423 .30519 Mdot 36085 .30519 Mdot 37941 .30519 Mdot 39796 .30519 Mdot 41651 .30519 Mdot 47217 .30519 Mdot 49072 .30519 Mdot 50928 .30519 Mdot 56494 .30519 Mdot 58349 .30519 Mdot 60204 .30519 Mdot 63915 .30519 Mdot 67625 .30519 Mdot 71336 .30519 Mdot 73191 .30519 Mdot 76902 .30519 Mdot 82468 .30519 Mdot 84323 .30519 Mdot 93599 .30519 Mdot 06401 .32375 Mdot 11967 .32375 Mdot 13822 .32375 Mdot 24954 .32375 Mdot 28664 .32375 Mdot 37941 .32375 Mdot 39796 .32375 Mdot 41651 .32375 Mdot 43506 .32375 Mdot 47217 .32375 Mdot 52783 .32375 Mdot 58349 .32375 Mdot 60204 .32375 Mdot 62059 .32375 Mdot 63915 .32375 Mdot 6577 .32375 Mdot 67625 .32375 Mdot 69481 .32375 Mdot 75046 .32375 Mdot 76902 .32375 Mdot 80612 .32375 Mdot 88033 .32375 Mdot 95455 .32375 Mdot 06401 .3423 Mdot 08256 .3423 Mdot 13822 .3423 Mdot 15677 .3423 Mdot 17532 .3423 Mdot 19388 .3423 Mdot 30519 .3423 Mdot 3423 .3423 Mdot 36085 .3423 Mdot 39796 .3423 Mdot 41651 .3423 Mdot 47217 .3423 Mdot 52783 .3423 Mdot 56494 .3423 Mdot 6577 .3423 Mdot 67625 .3423 Mdot 73191 .3423 Mdot 75046 .3423 Mdot 76902 .3423 Mdot 86178 .3423 Mdot 93599 .3423 Mdot 04545 .36085 Mdot 06401 .36085 Mdot 08256 .36085 Mdot 11967 .36085 Mdot 13822 .36085 Mdot 17532 .36085 Mdot 28664 .36085 Mdot 30519 .36085 Mdot 3423 .36085 Mdot 37941 .36085 Mdot 43506 .36085 Mdot 45362 .36085 Mdot 47217 .36085 Mdot 49072 .36085 Mdot 54638 .36085 Mdot 60204 .36085 Mdot 6577 .36085 Mdot 67625 .36085 Mdot 69481 .36085 Mdot 76902 .36085 Mdot 86178 .36085 Mdot 89889 .36085 Mdot 95455 .36085 Mdot 06401 .37941 Mdot 08256 .37941 Mdot 10111 .37941 Mdot 11967 .37941 Mdot 15677 .37941 Mdot 19388 .37941 Mdot 21243 .37941 Mdot 23098 .37941 Mdot 26809 .37941 Mdot 28664 .37941 Mdot 30519 .37941 Mdot 39796 .37941 Mdot 43506 .37941 Mdot 49072 .37941 Mdot 52783 .37941 Mdot 54638 .37941 Mdot 56494 .37941 Mdot 58349 .37941 Mdot 60204 .37941 Mdot 63915 .37941 Mdot 67625 .37941 Mdot 75046 .37941 Mdot 76902 .37941 Mdot 78757 .37941 Mdot 82468 .37941 Mdot 84323 .37941 Mdot 86178 .37941 Mdot 88033 .37941 Mdot 04545 .39796 Mdot 06401 .39796 Mdot 08256 .39796 Mdot 10111 .39796 Mdot 13822 .39796 Mdot 15677 .39796 Mdot 23098 .39796 Mdot 28664 .39796 Mdot 30519 .39796 Mdot 32375 .39796 Mdot 3423 .39796 Mdot 37941 .39796 Mdot 43506 .39796 Mdot 45362 .39796 Mdot 49072 .39796 Mdot 50928 .39796 Mdot 52783 .39796 Mdot 54638 .39796 Mdot 63915 .39796 Mdot 6577 .39796 Mdot 67625 .39796 Mdot 69481 .39796 Mdot 78757 .39796 Mdot 84323 .39796 Mdot 89889 .39796 Mdot 04545 .41651 Mdot 10111 .41651 Mdot 15677 .41651 Mdot 19388 .41651 Mdot 24954 .41651 Mdot 28664 .41651 Mdot 30519 .41651 Mdot 32375 .41651 Mdot 37941 .41651 Mdot 39796 .41651 Mdot 41651 .41651 Mdot 43506 .41651 Mdot 45362 .41651 Mdot 49072 .41651 Mdot 54638 .41651 Mdot 60204 .41651 Mdot 6577 .41651 Mdot 67625 .41651 Mdot 69481 .41651 Mdot 71336 .41651 Mdot 84323 .41651 Mdot 86178 .41651 Mdot 88033 .41651 Mdot 89889 .41651 Mdot 91744 .41651 Mdot 93599 .41651 Mdot 95455 .41651 Mdot 06401 .43506 Mdot 10111 .43506 Mdot 11967 .43506 Mdot 15677 .43506 Mdot 17532 .43506 Mdot 19388 .43506 Mdot 21243 .43506 Mdot 24954 .43506 Mdot 26809 .43506 Mdot 30519 .43506 Mdot 32375 .43506 Mdot 36085 .43506 Mdot 37941 .43506 Mdot 41651 .43506 Mdot 43506 .43506 Mdot 50928 .43506 Mdot 54638 .43506 Mdot 56494 .43506 Mdot 58349 .43506 Mdot 63915 .43506 Mdot 67625 .43506 Mdot 69481 .43506 Mdot 71336 .43506 Mdot 75046 .43506 Mdot 76902 .43506 Mdot 78757 .43506 Mdot 80612 .43506 Mdot 82468 .43506 Mdot 86178 .43506 Mdot 88033 .43506 Mdot 89889 .43506 Mdot 91744 .43506 Mdot 95455 .43506 Mdot 04545 .45362 Mdot 10111 .45362 Mdot 11967 .45362 Mdot 19388 .45362 Mdot 24954 .45362 Mdot 26809 .45362 Mdot 30519 .45362 Mdot 32375 .45362 Mdot 36085 .45362 Mdot 47217 .45362 Mdot 50928 .45362 Mdot 52783 .45362 Mdot 54638 .45362 Mdot 56494 .45362 Mdot 58349 .45362 Mdot 60204 .45362 Mdot 63915 .45362 Mdot 6577 .45362 Mdot 71336 .45362 Mdot 73191 .45362 Mdot 75046 .45362 Mdot 78757 .45362 Mdot 80612 .45362 Mdot 82468 .45362 Mdot 88033 .45362 Mdot 89889 .45362 Mdot 93599 .45362 Mdot 04545 .47217 Mdot 06401 .47217 Mdot 08256 .47217 Mdot 10111 .47217 Mdot 11967 .47217 Mdot 13822 .47217 Mdot 19388 .47217 Mdot 24954 .47217 Mdot 26809 .47217 Mdot 30519 .47217 Mdot 3423 .47217 Mdot 36085 .47217 Mdot 39796 .47217 Mdot 45362 .47217 Mdot 47217 .47217 Mdot 50928 .47217 Mdot 52783 .47217 Mdot 58349 .47217 Mdot 63915 .47217 Mdot 6577 .47217 Mdot 71336 .47217 Mdot 73191 .47217 Mdot 75046 .47217 Mdot 86178 .47217 Mdot 91744 .47217 Mdot 93599 .47217 Mdot 08256 .49072 Mdot 13822 .49072 Mdot 17532 .49072 Mdot 21243 .49072 Mdot 23098 .49072 Mdot 24954 .49072 Mdot 26809 .49072 Mdot 30519 .49072 Mdot 3423 .49072 Mdot 36085 .49072 Mdot 37941 .49072 Mdot 39796 .49072 Mdot 41651 .49072 Mdot 47217 .49072 Mdot 49072 .49072 Mdot 50928 .49072 Mdot 54638 .49072 Mdot 71336 .49072 Mdot 73191 .49072 Mdot 78757 .49072 Mdot 84323 .49072 Mdot 86178 .49072 Mdot 88033 .49072 Mdot 91744 .49072 Mdot 93599 .49072 Mdot 95455 .49072 Mdot 04545 .50928 Mdot 06401 .50928 Mdot 11967 .50928 Mdot 13822 .50928 Mdot 15677 .50928 Mdot 24954 .50928 Mdot 36085 .50928 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