Graphs drawn with Laplacian eigenvectors

3527 days ago by butler

def TreeDecLap(graph): l = graph.laplacian_matrix() eigs = l.eigenvectors_right() bananas = {} for i in range(len(eigs)): bananas[eigs[i][0]] = eigs[i] evals = bananas.keys() evals.sort() if bananas[evals[1]][2]==1 and bananas[evals[2]][2]==1: f=list(bananas[evals[1]][1][0]) g=list(bananas[evals[2]][1][0]) len_f = sqrt(sum([x^2 for x in f])) len_g = sqrt(sum([x^2 for x in g])) points = [] for i in range(len(f)): points.append((f[i]/len_f,g[i]/len_g)) return points if bananas[evals[1]][2]==2: f=list(bananas[evals[1]][1][0]) g=list(bananas[evals[1]][1][1]) t=sum([f[i]*g[i] for i in range(len(f))])/sum([f[i]*f[i] for i in range(len(f))]) new_g=[g[i]-t*f[i] for i in range(len(f))] len_f = sqrt(sum([x^2 for x in f])) len_new_g = sqrt(sum([x^2 for x in new_g])) points = [] for i in range(len(f)): points.append((f[i]/len_f,new_g[i]/len_new_g)) return points return False # failed to make anything happen! 
       
def draw_graph(graph,points_sharp): points=[] for p in points_sharp: points.append((p[0].n(digits=5),p[1].n(digits=5))) P = point(points,size=125) for e in graph.edges(): P += line([points[e[0]],points[e[1]]]) return P 
       
from sage.graphs.graph import Graph import networkx.generators.atlas W = [Graph(i) for i in networkx.generators.atlas.graph_atlas_g()] 
       
%time html('<!--notruncate-->') for i in range(4,len(W)): G=W[i] if G.is_connected(): q = TreeDecLap(G) if q: print "Atlas of Graphs: G"+str(i) G.show() draw_graph(G,q) print "\n===========================\n" 
       
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Atlas of Graphs:  G890


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Atlas of Graphs:  G899


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Atlas of Graphs:  G1022


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Atlas of Graphs:  G1036


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Atlas of Graphs:  G1039


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Atlas of Graphs:  G1051


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Atlas of Graphs:  G1061


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Atlas of Graphs:  G1065


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Atlas of Graphs:  G1066


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===========================

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Atlas of Graphs:  G1071


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Atlas of Graphs:  G1075


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Atlas of Graphs:  G1082


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Atlas of Graphs:  G1083


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Atlas of Graphs:  G1084


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Atlas of Graphs:  G1086


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Atlas of Graphs:  G1087


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Atlas of Graphs:  G1089


===========================

Atlas of Graphs:  G1090


===========================

Atlas of Graphs:  G1091


===========================

Atlas of Graphs:  G1092


===========================

Atlas of Graphs:  G1093


===========================

Atlas of Graphs:  G1094


===========================

Atlas of Graphs:  G1095


===========================

Atlas of Graphs:  G1096


===========================

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===========================

Atlas of Graphs:  G1098


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Atlas of Graphs:  G1099


===========================

Atlas of Graphs:  G1100


===========================

Atlas of Graphs:  G1101


===========================

Atlas of Graphs:  G1102


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Atlas of Graphs:  G1104


===========================

Atlas of Graphs:  G1105


===========================

Atlas of Graphs:  G1106


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Atlas of Graphs:  G1108


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Atlas of Graphs:  G1109


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Atlas of Graphs:  G1112


===========================

Atlas of Graphs:  G1113


===========================

Atlas of Graphs:  G1114


===========================

Atlas of Graphs:  G1115


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===========================

Atlas of Graphs:  G1118


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Atlas of Graphs:  G1119


===========================

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===========================

Atlas of Graphs:  G1121


===========================

Atlas of Graphs:  G1122


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Atlas of Graphs:  G1124


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Atlas of Graphs:  G1129


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Atlas of Graphs:  G1136


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Atlas of Graphs:  G1138


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Atlas of Graphs:  G1139


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Atlas of Graphs:  G1141


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Atlas of Graphs:  G1142


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Atlas of Graphs:  G1143


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Atlas of Graphs:  G1145


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Atlas of Graphs:  G1146


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Atlas of Graphs:  G1147


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Atlas of Graphs:  G1148


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Atlas of Graphs:  G1149


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Atlas of Graphs:  G1151


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Atlas of Graphs:  G1154


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Atlas of Graphs:  G1155


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Atlas of Graphs:  G1156


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Atlas of Graphs:  G1159


===========================

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===========================

Atlas of Graphs:  G1161


===========================

Atlas of Graphs:  G1162


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Atlas of Graphs:  G1163


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Atlas of Graphs:  G1164


===========================

Atlas of Graphs:  G1165


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Atlas of Graphs:  G1166


===========================

Atlas of Graphs:  G1167


===========================

Atlas of Graphs:  G1168


===========================

Atlas of Graphs:  G1170


===========================

Atlas of Graphs:  G1173


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Atlas of Graphs:  G1174


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Atlas of Graphs:  G1175


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===========================

Atlas of Graphs:  G1177


===========================

Atlas of Graphs:  G1179


===========================

Atlas of Graphs:  G1180


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Atlas of Graphs:  G1181


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Atlas of Graphs:  G1182


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Atlas of Graphs:  G1183


===========================

Atlas of Graphs:  G1185


===========================

Atlas of Graphs:  G1186


===========================

Atlas of Graphs:  G1187


===========================

Atlas of Graphs:  G1188


===========================

Atlas of Graphs:  G1189


===========================

Atlas of Graphs:  G1190


===========================

Atlas of Graphs:  G1192


===========================

Atlas of Graphs:  G1193


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Atlas of Graphs:  G1194


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Atlas of Graphs:  G1195


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Atlas of Graphs:  G1196


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Atlas of Graphs:  G1198


===========================

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Atlas of Graphs:  G1200


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Atlas of Graphs:  G1201


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Atlas of Graphs:  G1202


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Atlas of Graphs:  G1204


===========================

Atlas of Graphs:  G1209


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Atlas of Graphs:  G1211


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Atlas of Graphs:  G1212


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Atlas of Graphs:  G1214


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Atlas of Graphs:  G1215


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Atlas of Graphs:  G1216


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Atlas of Graphs:  G1217


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Atlas of Graphs:  G1218


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Atlas of Graphs:  G1219


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Atlas of Graphs:  G1220


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Atlas of Graphs:  G1221


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Atlas of Graphs:  G1222


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Atlas of Graphs:  G1223


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Atlas of Graphs:  G1224


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Atlas of Graphs:  G1225


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Atlas of Graphs:  G1226


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Atlas of Graphs:  G1227


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Atlas of Graphs:  G1228


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Atlas of Graphs:  G1231


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Atlas of Graphs:  G1232


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Atlas of Graphs:  G1233


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Atlas of Graphs:  G1235


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Atlas of Graphs:  G1236


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Atlas of Graphs:  G1237


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Atlas of Graphs:  G1239


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Atlas of Graphs:  G1240


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Atlas of Graphs:  G1242


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Atlas of Graphs:  G1245


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Atlas of Graphs:  G1246


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Atlas of Graphs:  G1247


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Atlas of Graphs:  G1249


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Atlas of Graphs:  G1250


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CPU time: 645.71 s,  Wall time: 646.20 s