Multilevel agglomerative edge bundling (MINGLE).
Arguments
- object
a graph object (igraph/network/tbl_graph)
- xy
coordinates of vertices
- k
number of nearest neighbours considered as merge candidates per edge
- segments
number of points sampled per bundled edge
- bundle_strength
strength of bundling between 0 (straight edges) and 1 (route fully through the meeting points)
Details
Groups edges bottom-up: two bundles are merged whenever routing them through shared meeting points reduces the total drawn length ("ink"). Meeting points are the geometric medians of the source-side and target-side endpoints. A kNN proximity graph over the edges is built once with a kd-tree and then coarsened level by level (O(E log E)).
see online for plotting tips
References
Gansner, Emden R., Yifan Hu, Stephen North, and Carlos Scheidegger. "Multilevel agglomerative edge bundling for visualizing large graphs." 2011 IEEE Pacific Visualization Symposium (2011): 187-194.
Examples
library(igraph)
g <- graph_from_edgelist(
matrix(c(1, 12, 2, 11, 3, 10, 4, 9, 5, 8, 6, 7), ncol = 2, byrow = TRUE), FALSE
)
xy <- cbind(c(rep(0, 6), rep(1, 6)), c(1:6, 1:6))
edge_bundle_mingle(g, xy)
#> x y index group
#> 1 0.00000000 1.000000 0.00000000 1
#> 2 0.11797220 1.014214 0.02040816 1
#> 3 0.23594441 1.028427 0.04081633 1
#> 4 0.35391661 1.042641 0.06122449 1
#> 5 0.46324008 1.066200 0.08163265 1
#> 6 0.47382678 1.184119 0.10204082 1
#> 7 0.47643770 1.302915 0.12244898 1
#> 8 0.47904862 1.421712 0.14285714 1
#> 9 0.48165953 1.540509 0.16326531 1
#> 10 0.49169749 1.658487 0.18367347 1
#> 11 0.49476304 1.777040 0.20408163 1
#> 12 0.49512421 1.895865 0.22448980 1
#> 13 0.49548538 2.014690 0.24489796 1
#> 14 0.49584655 2.133515 0.26530612 1
#> 15 0.49620772 2.252340 0.28571429 1
#> 16 0.49656889 2.371164 0.30612245 1
#> 17 0.49693006 2.489989 0.32653061 1
#> 18 0.49729123 2.608814 0.34693878 1
#> 19 0.49765240 2.727639 0.36734694 1
#> 20 0.49801357 2.846464 0.38775510 1
#> 21 0.49837474 2.965288 0.40816327 1
#> 22 0.49873591 3.084113 0.42857143 1
#> 23 0.49909708 3.202938 0.44897959 1
#> 24 0.49945825 3.321763 0.46938776 1
#> 25 0.49981942 3.440588 0.48979592 1
#> 26 0.50018058 3.559412 0.51020408 1
#> 27 0.50054175 3.678237 0.53061224 1
#> 28 0.50090292 3.797062 0.55102041 1
#> 29 0.50126409 3.915887 0.57142857 1
#> 30 0.50162526 4.034712 0.59183673 1
#> 31 0.50198643 4.153536 0.61224490 1
#> 32 0.50234760 4.272361 0.63265306 1
#> 33 0.50270877 4.391186 0.65306122 1
#> 34 0.50306994 4.510011 0.67346939 1
#> 35 0.50343111 4.628836 0.69387755 1
#> 36 0.50379228 4.747660 0.71428571 1
#> 37 0.50415345 4.866485 0.73469388 1
#> 38 0.50451462 4.985310 0.75510204 1
#> 39 0.50487579 5.104135 0.77551020 1
#> 40 0.50523696 5.222960 0.79591837 1
#> 41 0.50830251 5.341513 0.81632653 1
#> 42 0.51834047 5.459491 0.83673469 1
#> 43 0.52095138 5.578288 0.85714286 1
#> 44 0.52356230 5.697085 0.87755102 1
#> 45 0.52617322 5.815881 0.89795918 1
#> 46 0.53675992 5.933800 0.91836735 1
#> 47 0.64608339 5.957359 0.93877551 1
#> 48 0.76405559 5.971573 0.95918367 1
#> 49 0.88202780 5.985786 0.97959184 1
#> 50 1.00000000 6.000000 1.00000000 1
#> 51 0.00000000 2.000000 0.00000000 2
#> 52 0.11260726 2.008140 0.02040816 2
#> 53 0.22521453 2.016281 0.04081633 2
#> 54 0.33782179 2.024421 0.06122449 2
#> 55 0.45042906 2.032561 0.08163265 2
#> 56 0.47400971 1.999636 0.10204082 2
#> 57 0.47701934 1.886775 0.12244898 2
#> 58 0.48002897 1.773914 0.14285714 2
#> 59 0.48303859 1.661053 0.16326531 2
#> 60 0.49464844 1.750041 0.18367347 2
#> 61 0.49499371 1.862942 0.20408163 2
#> 62 0.49533897 1.975842 0.22448980 2
#> 63 0.49568423 2.088743 0.24489796 2
#> 64 0.49602949 2.201643 0.26530612 2
#> 65 0.49637475 2.314544 0.28571429 2
#> 66 0.49672001 2.427444 0.30612245 2
#> 67 0.49706528 2.540345 0.32653061 2
#> 68 0.49741054 2.653246 0.34693878 2
#> 69 0.49775580 2.766146 0.36734694 2
#> 70 0.49810106 2.879047 0.38775510 2
#> 71 0.49844632 2.991947 0.40816327 2
#> 72 0.49879158 3.104848 0.42857143 2
#> 73 0.49913685 3.217749 0.44897959 2
#> 74 0.49948211 3.330649 0.46938776 2
#> 75 0.49982737 3.443550 0.48979592 2
#> 76 0.50017263 3.556450 0.51020408 2
#> 77 0.50051789 3.669351 0.53061224 2
#> 78 0.50086315 3.782251 0.55102041 2
#> 79 0.50120842 3.895152 0.57142857 2
#> 80 0.50155368 4.008053 0.59183673 2
#> 81 0.50189894 4.120953 0.61224490 2
#> 82 0.50224420 4.233854 0.63265306 2
#> 83 0.50258946 4.346754 0.65306122 2
#> 84 0.50293472 4.459655 0.67346939 2
#> 85 0.50327999 4.572556 0.69387755 2
#> 86 0.50362525 4.685456 0.71428571 2
#> 87 0.50397051 4.798357 0.73469388 2
#> 88 0.50431577 4.911257 0.75510204 2
#> 89 0.50466103 5.024158 0.77551020 2
#> 90 0.50500629 5.137058 0.79591837 2
#> 91 0.50535156 5.249959 0.81632653 2
#> 92 0.51696141 5.338947 0.83673469 2
#> 93 0.51997103 5.226086 0.85714286 2
#> 94 0.52298066 5.113225 0.87755102 2
#> 95 0.52599029 5.000364 0.89795918 2
#> 96 0.54957094 4.967439 0.91836735 2
#> 97 0.66217821 4.975579 0.93877551 2
#> 98 0.77478547 4.983719 0.95918367 2
#> 99 0.88739274 4.991860 0.97959184 2
#> 100 1.00000000 5.000000 1.00000000 2
#> 101 0.00000000 3.000000 0.00000000 3
#> 102 0.02040816 3.020408 0.02040816 3
#> 103 0.04081633 3.040816 0.04081633 3
#> 104 0.06122449 3.061224 0.06122449 3
#> 105 0.08163265 3.081633 0.08163265 3
#> 106 0.10204082 3.102041 0.10204082 3
#> 107 0.12244898 3.122449 0.12244898 3
#> 108 0.14285714 3.142857 0.14285714 3
#> 109 0.16326531 3.163265 0.16326531 3
#> 110 0.18367347 3.183673 0.18367347 3
#> 111 0.20408163 3.204082 0.20408163 3
#> 112 0.22448980 3.224490 0.22448980 3
#> 113 0.24489796 3.244898 0.24489796 3
#> 114 0.26530612 3.265306 0.26530612 3
#> 115 0.28571429 3.285714 0.28571429 3
#> 116 0.30612245 3.306122 0.30612245 3
#> 117 0.32653061 3.326531 0.32653061 3
#> 118 0.34693878 3.346939 0.34693878 3
#> 119 0.36734694 3.367347 0.36734694 3
#> 120 0.38775510 3.387755 0.38775510 3
#> 121 0.40816327 3.408163 0.40816327 3
#> 122 0.42857143 3.428571 0.42857143 3
#> 123 0.44897959 3.448980 0.44897959 3
#> 124 0.46938776 3.469388 0.46938776 3
#> 125 0.48979592 3.489796 0.48979592 3
#> 126 0.51020408 3.510204 0.51020408 3
#> 127 0.53061224 3.530612 0.53061224 3
#> 128 0.55102041 3.551020 0.55102041 3
#> 129 0.57142857 3.571429 0.57142857 3
#> 130 0.59183673 3.591837 0.59183673 3
#> 131 0.61224490 3.612245 0.61224490 3
#> 132 0.63265306 3.632653 0.63265306 3
#> 133 0.65306122 3.653061 0.65306122 3
#> 134 0.67346939 3.673469 0.67346939 3
#> 135 0.69387755 3.693878 0.69387755 3
#> 136 0.71428571 3.714286 0.71428571 3
#> 137 0.73469388 3.734694 0.73469388 3
#> 138 0.75510204 3.755102 0.75510204 3
#> 139 0.77551020 3.775510 0.77551020 3
#> 140 0.79591837 3.795918 0.79591837 3
#> 141 0.81632653 3.816327 0.81632653 3
#> 142 0.83673469 3.836735 0.83673469 3
#> 143 0.85714286 3.857143 0.85714286 3
#> 144 0.87755102 3.877551 0.87755102 3
#> 145 0.89795918 3.897959 0.89795918 3
#> 146 0.91836735 3.918367 0.91836735 3
#> 147 0.93877551 3.938776 0.93877551 3
#> 148 0.95918367 3.959184 0.95918367 3
#> 149 0.97959184 3.979592 0.97959184 3
#> 150 1.00000000 4.000000 1.00000000 3
#> 151 0.00000000 4.000000 0.00000000 4
#> 152 0.02040816 3.979592 0.02040816 4
#> 153 0.04081633 3.959184 0.04081633 4
#> 154 0.06122449 3.938776 0.06122449 4
#> 155 0.08163265 3.918367 0.08163265 4
#> 156 0.10204082 3.897959 0.10204082 4
#> 157 0.12244898 3.877551 0.12244898 4
#> 158 0.14285714 3.857143 0.14285714 4
#> 159 0.16326531 3.836735 0.16326531 4
#> 160 0.18367347 3.816327 0.18367347 4
#> 161 0.20408163 3.795918 0.20408163 4
#> 162 0.22448980 3.775510 0.22448980 4
#> 163 0.24489796 3.755102 0.24489796 4
#> 164 0.26530612 3.734694 0.26530612 4
#> 165 0.28571429 3.714286 0.28571429 4
#> 166 0.30612245 3.693878 0.30612245 4
#> 167 0.32653061 3.673469 0.32653061 4
#> 168 0.34693878 3.653061 0.34693878 4
#> 169 0.36734694 3.632653 0.36734694 4
#> 170 0.38775510 3.612245 0.38775510 4
#> 171 0.40816327 3.591837 0.40816327 4
#> 172 0.42857143 3.571429 0.42857143 4
#> 173 0.44897959 3.551020 0.44897959 4
#> 174 0.46938776 3.530612 0.46938776 4
#> 175 0.48979592 3.510204 0.48979592 4
#> 176 0.51020408 3.489796 0.51020408 4
#> 177 0.53061224 3.469388 0.53061224 4
#> 178 0.55102041 3.448980 0.55102041 4
#> 179 0.57142857 3.428571 0.57142857 4
#> 180 0.59183673 3.408163 0.59183673 4
#> 181 0.61224490 3.387755 0.61224490 4
#> 182 0.63265306 3.367347 0.63265306 4
#> 183 0.65306122 3.346939 0.65306122 4
#> 184 0.67346939 3.326531 0.67346939 4
#> 185 0.69387755 3.306122 0.69387755 4
#> 186 0.71428571 3.285714 0.71428571 4
#> 187 0.73469388 3.265306 0.73469388 4
#> 188 0.75510204 3.244898 0.75510204 4
#> 189 0.77551020 3.224490 0.77551020 4
#> 190 0.79591837 3.204082 0.79591837 4
#> 191 0.81632653 3.183673 0.81632653 4
#> 192 0.83673469 3.163265 0.83673469 4
#> 193 0.85714286 3.142857 0.85714286 4
#> 194 0.87755102 3.122449 0.87755102 4
#> 195 0.89795918 3.102041 0.89795918 4
#> 196 0.91836735 3.081633 0.91836735 4
#> 197 0.93877551 3.061224 0.93877551 4
#> 198 0.95918367 3.040816 0.95918367 4
#> 199 0.97959184 3.020408 0.97959184 4
#> 200 1.00000000 3.000000 1.00000000 4
#> 201 0.00000000 5.000000 0.00000000 5
#> 202 0.11260726 4.991860 0.02040816 5
#> 203 0.22521453 4.983719 0.04081633 5
#> 204 0.33782179 4.975579 0.06122449 5
#> 205 0.45042906 4.967439 0.08163265 5
#> 206 0.47400971 5.000364 0.10204082 5
#> 207 0.47701934 5.113225 0.12244898 5
#> 208 0.48002897 5.226086 0.14285714 5
#> 209 0.48303859 5.338947 0.16326531 5
#> 210 0.49464844 5.249959 0.18367347 5
#> 211 0.49499371 5.137058 0.20408163 5
#> 212 0.49533897 5.024158 0.22448980 5
#> 213 0.49568423 4.911257 0.24489796 5
#> 214 0.49602949 4.798357 0.26530612 5
#> 215 0.49637475 4.685456 0.28571429 5
#> 216 0.49672001 4.572556 0.30612245 5
#> 217 0.49706528 4.459655 0.32653061 5
#> 218 0.49741054 4.346754 0.34693878 5
#> 219 0.49775580 4.233854 0.36734694 5
#> 220 0.49810106 4.120953 0.38775510 5
#> 221 0.49844632 4.008053 0.40816327 5
#> 222 0.49879158 3.895152 0.42857143 5
#> 223 0.49913685 3.782251 0.44897959 5
#> 224 0.49948211 3.669351 0.46938776 5
#> 225 0.49982737 3.556450 0.48979592 5
#> 226 0.50017263 3.443550 0.51020408 5
#> 227 0.50051789 3.330649 0.53061224 5
#> 228 0.50086315 3.217749 0.55102041 5
#> 229 0.50120842 3.104848 0.57142857 5
#> 230 0.50155368 2.991947 0.59183673 5
#> 231 0.50189894 2.879047 0.61224490 5
#> 232 0.50224420 2.766146 0.63265306 5
#> 233 0.50258946 2.653246 0.65306122 5
#> 234 0.50293472 2.540345 0.67346939 5
#> 235 0.50327999 2.427444 0.69387755 5
#> 236 0.50362525 2.314544 0.71428571 5
#> 237 0.50397051 2.201643 0.73469388 5
#> 238 0.50431577 2.088743 0.75510204 5
#> 239 0.50466103 1.975842 0.77551020 5
#> 240 0.50500629 1.862942 0.79591837 5
#> 241 0.50535156 1.750041 0.81632653 5
#> 242 0.51696141 1.661053 0.83673469 5
#> 243 0.51997103 1.773914 0.85714286 5
#> 244 0.52298066 1.886775 0.87755102 5
#> 245 0.52599029 1.999636 0.89795918 5
#> 246 0.54957094 2.032561 0.91836735 5
#> 247 0.66217821 2.024421 0.93877551 5
#> 248 0.77478547 2.016281 0.95918367 5
#> 249 0.88739274 2.008140 0.97959184 5
#> 250 1.00000000 2.000000 1.00000000 5
#> 251 0.00000000 6.000000 0.00000000 6
#> 252 0.11797220 5.985786 0.02040816 6
#> 253 0.23594441 5.971573 0.04081633 6
#> 254 0.35391661 5.957359 0.06122449 6
#> 255 0.46324008 5.933800 0.08163265 6
#> 256 0.47382678 5.815881 0.10204082 6
#> 257 0.47643770 5.697085 0.12244898 6
#> 258 0.47904862 5.578288 0.14285714 6
#> 259 0.48165953 5.459491 0.16326531 6
#> 260 0.49169749 5.341513 0.18367347 6
#> 261 0.49476304 5.222960 0.20408163 6
#> 262 0.49512421 5.104135 0.22448980 6
#> 263 0.49548538 4.985310 0.24489796 6
#> 264 0.49584655 4.866485 0.26530612 6
#> 265 0.49620772 4.747660 0.28571429 6
#> 266 0.49656889 4.628836 0.30612245 6
#> 267 0.49693006 4.510011 0.32653061 6
#> 268 0.49729123 4.391186 0.34693878 6
#> 269 0.49765240 4.272361 0.36734694 6
#> 270 0.49801357 4.153536 0.38775510 6
#> 271 0.49837474 4.034712 0.40816327 6
#> 272 0.49873591 3.915887 0.42857143 6
#> 273 0.49909708 3.797062 0.44897959 6
#> 274 0.49945825 3.678237 0.46938776 6
#> 275 0.49981942 3.559412 0.48979592 6
#> 276 0.50018058 3.440588 0.51020408 6
#> 277 0.50054175 3.321763 0.53061224 6
#> 278 0.50090292 3.202938 0.55102041 6
#> 279 0.50126409 3.084113 0.57142857 6
#> 280 0.50162526 2.965288 0.59183673 6
#> 281 0.50198643 2.846464 0.61224490 6
#> 282 0.50234760 2.727639 0.63265306 6
#> 283 0.50270877 2.608814 0.65306122 6
#> 284 0.50306994 2.489989 0.67346939 6
#> 285 0.50343111 2.371164 0.69387755 6
#> 286 0.50379228 2.252340 0.71428571 6
#> 287 0.50415345 2.133515 0.73469388 6
#> 288 0.50451462 2.014690 0.75510204 6
#> 289 0.50487579 1.895865 0.77551020 6
#> 290 0.50523696 1.777040 0.79591837 6
#> 291 0.50830251 1.658487 0.81632653 6
#> 292 0.51834047 1.540509 0.83673469 6
#> 293 0.52095138 1.421712 0.85714286 6
#> 294 0.52356230 1.302915 0.87755102 6
#> 295 0.52617322 1.184119 0.89795918 6
#> 296 0.53675992 1.066200 0.91836735 6
#> 297 0.64608339 1.042641 0.93877551 6
#> 298 0.76405559 1.028427 0.95918367 6
#> 299 0.88202780 1.014214 0.97959184 6
#> 300 1.00000000 1.000000 1.00000000 6