R 绘制非重叠最小生成树

问题描述

我创建了一个最小生成树，其中使用 Louvain 方法找到了社区。我现在想清楚地显示树，也就是说，如果有一个无重叠的表示会很棒。

左边是我当前的情节，右边是 Wang 等人的一个很好的例子。 （2017 年，JEIC），这更清晰，而且大部分不重叠。

我想知道如何更清楚地表示这棵树，特别是必须注意，这种表示只是一个MWE，实际表示有更多的观察。

MWE：

library(igraph)
lstat <- c(4.98,9.14,4.03,2.94,5.33,5.21,12.43,19.15,29.93,17.1,20.45,13.27,15.71,8.26,10.26,8.47,6.58,14.67,11.69,11.28,21.02,13.83,18.72,19.88,16.3,16.51,14.81,17.28,12.8,11.98,22.6,13.04,27.71,18.35,20.34,9.68,11.41,8.77,10.13,4.32,1.98,4.84,5.81,7.44,9.55,10.21,14.15,18.8,30.81,16.2,13.45,9.43,5.28,8.43,14.8,4.81,5.77,3.95,6.86,9.22,13.15,14.44,6.73,9.5,8.05,4.67,10.24,8.1,13.09,8.79,6.72,9.88,5.52,7.54,6.78,8.94,11.97,10.27,12.34,9.1,5.29,7.22,7.51,9.62,6.53,12.86,8.44,5.5,5.7,8.81,8.2,8.16,6.21,10.59,6.65,11.34,4.21,3.57,6.19,9.42,7.67,10.63,13.44,12.33,16.47,18.66,14.09,12.27,15.55,13,10.16,16.21,17.09,10.45,15.76,12.04,10.3,15.37,13.61,14.37,14.27,17.93,25.41,17.58,27.26,17.19,15.39,18.34,12.6,12.26,11.12,15.03,17.31,16.96,16.9,14.59,21.32,18.46,24.16,34.41,26.82,26.42,29.29,27.8,16.65,29.53,28.32,21.45,14.1,13.28,12.12,15.79,15.12,15.02,16.14,4.59,6.43,7.39,1.73,1.92,3.32,11.64,9.81,3.7,12.14,11.1,11.32,14.43,12.03,14.69,9.04,9.64,10.11,6.29,6.92,5.04,7.56,9.45,4.82,5.68,13.98,4.45,6.68,4.56,5.39,5.1,4.69,2.87,5.03,4.38,2.97,4.08,8.61,6.62,7.43,3.11,3.81,2.88,10.87,10.97,18.06,14.66,23.09,17.27,23.98,16.03,9.38,29.55,9.47,13.51,9.69,17.92,10.5,9.71,21.46,9.93,7.6,4.14,4.63,3.13,6.36,3.92,3.76,11.65,5.25,2.47,10.88,9.54,4.73,7.37,11.38,12.4,11.22,5.19,12.5,9.16,10.15,9.52,6.56,5.9,3.59,3.53,3.54,6.57,9.25,5.12,7.79,6.9,9.59,7.26,5.91,11.25,14.79,3.16,13.65,6.59,7.73,2.98,6.05,4.16,7.19,4.85,3.01,7.85,8.23,12.93,7.14,9.51,3.33,3.56,4.7,8.58,10.4,6.27,15.84,4.97,4.74,6.07,8.67,4.86,6.93,8.93,6.47,7.53,4.54,9.97,12.64,5.98,11.72,7.9,9.28,11.5,18.33,15.94,10.36,12.73,7.2,6.87,7.7,11.74,6.12,5.08,6.15,12.79,7.34,9.09,7.83,6.75,8.01,9.8,10.56,8.51,9.74,9.29,5.49,8.65,7.18,4.61,10.53,12.67,5.99,5.89,4.5,5.57,17.6,11.48,14.19,10.19,14.64,7.12,14,13.33,3.26,3.73,2.96,9.53,8.88,34.77,37.97,23.24,21.24,23.69,21.78,17.21,21.08,23.6,24.56,30.63,28.28,31.99,30.62,20.85,17.11,18.76,25.68,15.17,16.35,17.12,19.37,19.92,30.59,29.97,26.77,20.32,20.31,19.77,27.38,22.98,23.34,12.13,26.4,19.78,21.22,34.37,20.08,36.98,29.05,25.79,26.64,20.62,22.74,15.7,23.29,17.16,24.39,15.69,14.52,21.52,24.08,17.64,19.69,16.22,23.27,18.05,26.45,34.02,22.88,22.11,19.52,16.59,18.85,23.79,17.79,16.44,18.13,19.31,17.44,17.73,16.74,18.71,19.01,16.94,16.23,14.7,16.42,14.65,13.99,10.29,13.22,14.13,17.15,14.76,16.29,12.87,14.36,11.66,18.14,24.1,18.68,24.91,18.03,13.11,10.74,7.74,7.01,10.42,13.34,10.58,14.98,11.45,23.97,29.68,18.07,13.35,12.01,13.59,21.14,12.92,15.1)
rm <- c(6.575,6.421,7.185,6.998,7.147,6.012,6.172,5.631,6.004,6.377,6.009,5.889,5.949,6.096,5.834,5.935,5.456,5.727,5.965,6.142,5.813,5.924,5.599,6.047,6.495,6.674,5.713,6.072,5.95,5.701,5.933,5.841,5.85,5.966,6.595,7.024,6.77,6.169,6.211,6.069,5.682,5.786,6.03,5.399,5.602,5.963,6.115,6.511,5.998,5.888,7.249,6.383,6.816,6.145,5.927,5.741,6.456,6.762,7.104,5.787,5.878,5.594,5.885,6.417,5.961,6.065,6.245,6.273,6.286,6.279,6.14,6.232,5.874,6.727,6.619,6.302,6.167,6.389,6.63,6.015,6.121,7.007,7.079,6.405,6.442,6.249,6.625,6.163,8.069,7.82,7.416,6.781,6.137,5.851,5.836,6.127,6.474,6.229,6.195,6.715,5.913,6.092,6.254,5.928,6.176,6.021,5.872,5.731,5.87,5.856,5.879,5.986,5.613,5.693,6.431,5.637,6.458,6.326,6.372,5.822,5.757,6.335,5.942,6.454,5.857,6.151,6.174,5.019,5.403,5.468,4.903,6.13,5.628,4.926,5.186,5.597,6.122,5.404,5.012,5.709,6.129,6.152,5.272,6.943,6.066,6.51,6.25,7.489,7.802,8.375,5.854,6.101,7.929,5.877,6.319,6.402,5.875,5.88,5.572,6.416,5.859,6.546,6.02,6.315,6.98,7.765,6.144,7.155,6.563,5.604,6.153,7.831,6.782,6.556,6.951,6.739,7.178,6.8,6.604,7.875,7.287,7.107,7.274,6.975,7.135,6.162,7.61,7.853,8.034,5.891,5.783,6.064,5.344,5.96,5.807,6.375,5.412,6.182,6.642,5.951,6.373,6.164,6.879,6.618,8.266,8.725,8.04,7.163,7.686,6.552,5.981,7.412,8.337,8.247,6.726,6.086,6.631,7.358,6.481,6.606,6.897,6.095,6.358,6.393,5.593,5.605,6.108,6.226,6.433,6.718,6.487,6.438,6.957,8.259,5.876,7.454,8.704,7.333,6.842,7.203,7.52,8.398,7.327,7.206,5.56,7.014,8.297,7.47,5.92,6.24,6.538,7.691,6.758,6.854,7.267,6.826,6.482,6.812,6.968,7.645,7.923,7.088,6.453,6.23,6.209,6.565,6.861,7.148,6.678,6.549,5.79,6.345,7.041,6.871,6.982,7.236,6.616,7.42,6.849,6.635,5.972,4.973,6.023,6.266,6.567,5.705,5.914,5.782,6.382,6.113,6.426,6.376,6.041,5.708,6.415,6.312,6.083,5.868,6.333,5.706,6.031,6.316,6.31,6.037,5.869,5.895,6.059,5.985,5.968,7.241,6.54,6.696,6.874,6.014,5.898,6.516,6.939,6.49,6.579,5.884,6.728,5.663,5.936,6.212,6.395,6.112,6.398,6.251,5.362,5.803,8.78,3.561,4.963,3.863,6.683,7.016,6.216,4.906,4.138,7.313,6.649,6.794,6.38,6.223,6.545,5.536,4.368,5.277,4.652,5,4.88,6.051,5.036,6.193,5.887,6.471,5.747,5.453,5.852,5.987,6.343,6.404,5.349,5.531,5.683,5.608,5.617,6.852,6.657,4.628,5.155,4.519,6.434,5.304,5.957,6.824,6.411,6.006,5.648,6.103,5.565,5.896,5.837,6.202,6.348,6.833,6.425,6.436,6.208,6.629,6.461,5.627,5.818,6.406,6.219,6.485,6.459,6.341,6.185,6.749,6.655,6.297,7.393,6.525,5.976,6.301,6.081,6.701,6.317,6.513,5.759,5.952,6.003,5.926,6.437,5.427,6.484,6.242,7.061,5.762,5.871,6.114,5.905,5.454,5.414,5.093,5.983,5.707,5.67,5.794,6.019,5.569)
dis <- c(4.09,4.9671,6.0622,5.5605,5.9505,6.0821,6.5921,6.3467,6.2267,5.4509,4.7075,4.4619,4.4986,4.2579,3.7965,3.7979,4.0123,3.9769,4.0952,4.3996,4.4546,4.682,4.4534,4.4547,4.239,4.233,4.175,3.99,3.7872,3.7598,3.3603,3.3779,3.9342,3.8473,5.4011,5.7209,5.1004,5.6894,6.0877,6.8147,7.3197,8.6966,9.1876,8.3248,7.8148,6.932,7.2254,6.8185,7.2255,7.9809,9.2229,6.6115,6.498,5.2873,4.2515,4.5026,4.0522,4.0905,5.0141,5.4007,4.7794,4.4377,4.4272,3.7476,3.4217,3.4145,3.0923,3.0921,3.6659,3.615,3.4952,2.7778,2.8561,2.7147,2.421,2.1069,2.211,2.1224,2.4329,2.5451,2.6775,2.3534,2.548,2.2565,2.4631,2.7301,2.7474,2.4775,2.7592,2.2577,2.1974,2.0869,1.9444,2.0063,1.9929,1.7572,1.7883,1.8125,1.9799,2.1185,2.271,2.3274,2.4699,2.346,2.1107,1.9669,1.8498,1.6686,1.6687,1.6119,1.4394,1.3216,1.4118,1.3459,1.4191,1.5166,1.4608,1.5296,1.5257,1.618,1.5916,1.6102,1.6232,1.7494,1.7455,1.7364,1.8773,1.7573,1.7659,1.7984,1.9709,2.0407,2.162,2.422,2.2834,2.0459,2.4259,2.1,2.2625,2.3887,2.5961,2.6463,2.7019,3.1323,3.5549,3.3175,2.9153,2.829,2.741,2.5979,2.7006,2.847,2.9879,3.2797,3.1992,3.7886,4.5667,6.4798,6.2196,5.6484,7.309,7.6534,5.118,3.9454,4.3549,4.2392,3.875,3.8771,3.665,3.6526,3.5875,3.1121,3.4211,2.8893,3.3633,2.8617,3.048,3.2721,2.8944,3.2157,3.3751,3.6715,3.8384,3.6519,4.148,6.1899,6.3361,7.0355,7.9549,8.0555,7.8265,7.3967,8.9067,9.2203,1.801,1.8946,2.0107,2.1121,2.1398,2.2885,2.0788,1.9301,1.9865,2.1329,2.4216,2.872,3.9175,4.429,4.3665,4.0776,4.2673,4.7872,4.8628,4.1403,4.1007,4.6947,5.2447,5.2119,7.3073,9.0892,7.3172,5.1167,5.5027,5.9604,6.32,7.8278,5.4917,4.022,3.37,3.0992,3.1827,3.1025,2.5194,2.6403,2.834,3.2628,3.6023,3.945,3.9986,4.0317,3.5325,4.0019,4.5404,4.7211,5.4159,5.2146,5.8736,6.6407,6.4584,5.9853,5.2311,5.615,4.8122,7.0379,6.2669,5.7321,6.4654,8.0136,8.5353,8.344,8.7921,10.7103,12.1265,10.5857,2.1222,2.5052,2.7227,2.5091,2.5182,2.2955,2.1036,1.9047,1.6132,1.7523,1.5106,1.3325,1.3567,1.2024,1.1691,1.1296,1.1742,1.137,1.3163,1.3449,1.358,1.3861,1.4165,1.5192,1.5804,1.5331,1.4395,1.4261,1.4672,1.5184,1.5895,1.7281,1.9265,2.1678,1.77,1.7912,1.7821,1.7257,1.6768,1.6334,1.4896,1.5004,1.5888,1.5741,1.639,1.7028,1.6074,1.4254,1.1781,1.2852,1.4547,1.4655,1.413,1.5275,1.5539,1.5894,1.6582,1.8347,1.8195,1.6475,1.8026,1.794,1.8589,1.8746,1.9512,2.0218,2.0635,1.9096,1.9976,1.8629,1.9356,1.9682,2.0527,2.0882,2.2004,2.3158,2.2222,2.1247,2.0026,1.9142,1.8206,1.8172,1.8662,2.0651,2.0048,1.9784,1.8956,1.9879,2.072,2.198,2.2616,2.185,2.3236,2.3552,2.3682,2.4527,2.4961,2.4358,2.5806,2.7792,2.7831,2.7175,2.5975,2.5671,2.7344,2.8016,2.9634,3.0665,2.8715,2.5403,2.9084,2.8237,3.0334,3.0993,2.8965,2.5329,2.4298,2.206,2.3053,2.1007,2.1705,3.4242,3.3317,3.4106,4.0983,3.724,3.9917,3.5459,3.1523,1.8209,1.7554,1.8226,1.8681,2.1099,2.3817,2.7986,2.8927,2.4091,2.3999)
indus <- c(2.31,7.07,2.18,7.87,8.14,2.95,6.91,5.64,4,1.22,0.74,1.32,5.13,1.38,10.81,12.83,4.49,3.41,15.04,2.89,8.56,10.01,25.65,21.89,19.58,4.05,2.46,3.44,2.93,0.46,1.52,1.47,2.03,2.68,13.89,6.2,4.93,5.86,3.64,3.75,3.97,6.96,6.41,1.21,2.25,1.76,5.32,4.95,13.92,2.24,6.09,9.9,7.38,3.24,6.06,1.89,3.78,4.39,4.15,2.01,1.25,1.69,2.02,1.91,18.1,27.74,9.69)
from <- c(402,155,168,430,449,431,357,121,382,200,391,422,89,214,378,458,442,443,145,394,169,386,459,437,447,451,180,434,455,105,321,460,259,68,291,123,444,162,192,465,404,117,25,165,116,131,406,143,397,364,463,128,136,353,398,337,409,76,462,104,340,350,432,392,191,113,395,37,221,288,66,18,359,401,383,362,19,426,358,118,193,119,63,377,197,489,120,385,272,445,424,247,82,402,421,384,29,115,239,456,154,484,275,381,481,52,164,224,59,206,23,380,91,130,189,390,40,374,301,453,98,229,396,7,410,360,24,54,96,420,313,147,36,429,81,43,225,379,495,69,412,57,112,469,352,42,248,325,232,310,403,64,367,53,299,372,399,51,433,249,3,205,454,114,204,260,240,339,213,90,440,230,482,363,129,273,196,190,22,464,85,39,174,250,270,208,302,71,262,330,84,370,470,218,100,21,6,393,227,235,361,26,349,241,151,58,179,210,417,183,178,17,281,2,159,203,494,255,274,258,45,175,223,311,278,77,285,56,185,305,198,181,1,8,12,238,182,146,106,83,271,199,296,329,498,400,132,158,44,153,286,375,70,95,38,61,111,257,152,228,408,292,86,101,387,78,211,15,41,88,202,55,99,47,277,316,376,253,28,166,9,294,243,413,110,67,72,314,10,144,20,209,102,163,173,331,263,252,150,261,107,309,97,160,369,148,124,256,93,65,87,312,75,74,388,122,133,139,167,48,125,287,366,33,127,142,79,1)
to <- c(403,156,172,446,479,201,425,427,216,467,450,448,170,471,452,477,109,16,476,322,265,333,345,472,414,428,473,137,355,435,461,418,80,341,351,389,231,289,27,488,438,457,500,126,492,436,419,32,423,335,157,135,486,276,60,194,480,207,34,92,140,280,282,187,234,328,35,188,323,466,468,195,293,327,226,499,332,236,475,356,326,478,441,319,290,334,300,373,474,244,405,184,283,496,411,318,483,315,138,279,284,251,317,303,485,268,344,336,338,371,487,220,176,307,30,304,108,171,212,161,233,134,237,348,46,177,149,186,308,306,62,266,297,416,342,343,415,347,324,245,242,73,103,50,320,254,368,49,346,269,11,439,407,267,31,264,354,295,497,94,217,222,493,365,246,490,141,215,491,219,298,1)
distance <- c(0.0896270606457671,0.102685003773676,0.116158684565556,0.128953828946641,0.135274572629151,0.151398447812385,0.157880492778557,0.177741638340598,0.179479497436337,0.194164878389476,0.207781134851073,0.209260603076643,0.212687188142587,0.212953046467995,0.218858972856952,0.229946276334275,0.242068192871348,0.246678414134678,0.26707865882545,0.273143350642113,0.285823809365141,0.288804864917473,0.29018285614419,0.294646160674123,0.302718103191734,0.306487454881924,0.309049445882046,0.310647452910853,0.311192287822176,0.313034518863336,0.317748658533754,0.323222585844492,0.333766385365573,0.334880814619171,0.336881655778405,0.341719607280588,0.367789341879288,0.368402442988644,0.368462494699258,0.372747957740884,0.374743058641518,0.375990438708222,0.382028323557299,0.382877996233786,0.385621848447412,0.387688586367977,0.390832444917257,0.392281646269615,0.394263059390555,0.395322969228958,0.408219597765713,0.415163871260493,0.416266609278236,0.418746032817029,0.420286806835524,0.42139816088825,0.421899229674577,0.422761682275014,0.424695373179413,0.427081069587496,0.430952851249415,0.431260941890174,0.435407728456904,0.438786064044883,0.439022596229398,0.441977374986548,0.443086176719609,0.448269572913442,0.450320996623521,0.457931217542548,0.460176716055909,0.461297355292657,0.461566896559967,0.463421072028453,0.466282414422847,0.46947690039021,0.470107391986129,0.471181663480233,0.472055081531806,0.473546080123149,0.480153475463835,0.480405880480246,0.484499907120734,0.485293890338628,0.486389802524682,0.486815375681582,0.488394144109038,0.491468208534387,0.492655011138626,0.497034445486427,0.499496756746228,0.500525413940191,0.5088295981957,0.522619134743457,0.523084973976504,0.52588823907747,0.526474158910009,0.530203130884758,0.531195670163076,0.53228869046787,0.533614092767423,0.534514695775523,0.536015074414891,0.536343555941525,0.53634503819836,0.537032587465602,0.539637146608719,0.540169241997358,0.541938188357307,0.546300064067359,0.558594888984852,0.561035729699989,0.563712524253275,0.563726219010612,0.566597961521219,0.566755017622253,0.568176521866223,0.571212079704203,0.572649491399407,0.574042933934387,0.582635014395806,0.589662691714509,0.592021114488326,0.592210807061134,0.593764473507804,0.594393211603228,0.596242433914259,0.597323371382704,0.598675237503608,0.6000599970003,0.603565447983895,0.605146065012407,0.605735296973851,0.606108150415418,0.608646243724547,0.61011805415018,0.61273276393547,0.613181897971556,0.615542037557144,0.616392123570703,0.617162831025978,0.617621316018161,0.617623218475472,0.621880929117464,0.621900313555155,0.626290060594929,0.626464683761184,0.629007281356901,0.62945713912863,0.634054445611731,0.635753222563599,0.639139178896115,0.643531320139121,0.649846758859349,0.653886756250652,0.654327326343628,0.654436773111048,0.655769776674712,0.656412591286913,0.657747132262848,0.659657517201159,0.663896076204703,0.664269832221816,0.664651856237534,0.664927845709593,0.667246019096407,0.668030687917853,0.670801013714202,0.671402263922308,0.672684353913482,0.676978404382296,0.684548968299566,0.684926886609075,0.686732116621904,0.686907279041357,0.687072958280269,0.688186747910768,0.688376350552516,0.69149039038876,0.695538755210664,0.69672895734281,0.697456808698575,0.700946331754437,0.701562541759465,0.702524988879399,0.703033455818427,0.707367125331676,0.710703876449255,0.7153364592973,0.716412876768696,0.717987945581261,0.720230858822363,0.72026815145472,0.726222755082765,0.726274527985113,0.726972489163105,0.733018417231109,0.735079077378753,0.737372117726187,0.742266724297944,0.745306145151105,0.750870328352372,0.753696550343704,0.753996346144993,0.758206198866773,0.759598736175884,0.759616113573166,0.761828038339362,0.764076566843926,0.769583972026445,0.774298527701042,0.776035463107195,0.776443616755267,0.776778192278852,0.777992217184722,0.778428423170685,0.77882489045998,0.781196038136395,0.782117798033008,0.783427348258918,0.785290392148025,0.788300710389124,0.79280628781563,0.793295184657011,0.79409161310267,0.794847155118517,0.795576677637046,0.797399655129095,0.799595747862631,0.800425892884531,0.800766158126079,0.80119928232619,0.801516063469722,0.804285919309794,0.80647730284243,0.810483534687781,0.812394608549318,0.812447758320497,0.81327547608421,0.813646292930781,0.814599140682091,0.814924100760309,0.81773580085502,0.820171421106588,0.820573189910566,0.820785623655775,0.820989189941013,0.82959523262854,0.831624079737954,0.832532696054635,0.835419056521935,0.83784485437341,0.840925894475845,0.845896116553328,0.84662580281964,0.847087457114081,0.851853983966736,0.852993253197234,0.854853110189113,0.855454171770762,0.857189220650843,0.859844171928844,0.860539139144757,0.86469583669635,0.866583804372088,0.869813060375619,0.875525190956834,0.87765405485305,0.878692210048547,0.879442601879168,0.879821851285815,0.880241080613714,0.886502882116014,0.887798541336941,0.890845351337705,0.894158045314138,0.896890009978928,0.897374704345961,0.906979277602305,0.9083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df <- cbind.data.frame(lstat,rm,dis,indus,from,to,distance)
DistMat <- as.matrix(dist(df[,1:4],diag = T,upper = T))

g <- graph.data.frame(df[,5:6],directed = FALSE)
lou <- cluster_louvain(g)
set.seed(0)
plot(lou,g,vertex.label = NA,vertex.size = 5,mark.groups = NULL)

解决方法

首先，您的顶点比“nice”图中的顶点大得多。我将使用较小的节点大小。但重点是您应该指定布局。值得尝试的几个选项是 layout_as_tree 和 layout_with_gem。这是我得到的。

par(mfrow=c(1,2))
set.seed(20210401)
LOWG = layout_with_gem(g)
plot(lou,g,layout = LOWG,vertex.label = NA,vertex.size = 2.5,mark.groups = NULL,main="GEM")
LOAT = layout_as_tree(g)
plot(lou,layout = LOAT,main="TREE")

根据 OP 评论添加：

OP 注意到在创建图表时没有使用距离。使用距离取决于您的应用程序，但在图形显示中使用它最明显的方法是在顶点的布局中。您可能希望布局反映这些距离。这是一种方法。

您只提供边长，所以我们没有所有顶点之间的完整距离矩阵，但我们可以计算任何两个节点之间的最短加权路径的长度，并将其用作它们之间的距离。然后我们可以使用多维缩放以近似这些距离的方式来布局顶点。这是示例图表上的结果。

DistMat = distances(g,weights=distance)
set.seed(0)
LOMDS = layout_with_mds(g,dist=DistMat)
plot(lou,layout=LOMDS,main="MDS")