一、PageRank的基本思想

起源于網頁排名，如果有很多網頁(T)都有指向一個網頁(A)的鏈接，說明網頁(A)比較重要，如果沒有網頁指向網頁(A)，那么A就是孤零零的存在

二、PageRank算法的原理-基本概念

1、出鏈：網頁A可以跳轉到網頁B, 說明網頁A出鏈網頁B

2、入鏈：由A入鏈B

3、無出鏈: 沒有跳轉的鏈接到該網頁

4、只對自己出鏈：網頁的上有該網頁的鏈接

5、PR值：網頁被訪問的概率(Pagerank值)

三、PageRank算法的原理-出入鏈關系

四、pagerank算法公式的說明

四、馬爾科夫實例驗證

# -*- coding:utf-8 -*-'''@Author : wangtao@Time : 19/10/18 上午9:04@desc : '''import numpy as npdef markov():init_array = np.array([0.3, 0.2, 0.4, 0.1])transfer_matrix = np.array([[0, 0.5, 0, 0],[0.333, 0, 0, 0.5],[0.333, 0, 1, 0.5],[0.333, 0.5, 0, 0]])restmp = init_arrayfor i in range(100):res = 0.85 * np.dot(restmp,transfer_matrix) + 0.15 * restmpprint(i,"=====", res)restmp = resmarkov()0 ===== [0.243135 0.2 0.4 0.27 ] 1 ===== [0.28272375 0.24808238 0.4 0.2955 ] 2 ===== [0.30948955 0.28295745 0.4 0.31976001] 3 ===== [0.33024261 0.30987468 0.4 0.33822092] 4 ===== [0.34619985 0.3305782 0.4 0.35242988] 5 ===== [0.35847541 0.34650436 0.4 0.36336022] 6 ===== [0.36791848 0.3587558 0.4 0.37176839] 7 ===== [0.37518264 0.36818029 0.4 0.37823647] 8 ===== [0.38077066 0.37543017 0.4 0.38321209] 9 ===== [0.38506929 0.3810072 0.4 0.38703964] 10 ===== [0.38837605 0.38529737 0.4 0.389984 ] 11 ===== [0.3909198 0.38859763 0.4 0.39224898] 12 ===== [0.3928766 0.39113638 0.4 0.39399134] 13 ===== [0.39438189 0.39308933 0.4 0.39533166] 14 ===== [0.39553985 0.39459166 0.4 0.39636272] 15 ===== [0.39643061 0.39574734 0.4 0.39715586] 16 ===== [0.39711584 0.39663635 0.4 0.397766 ] 17 ===== [0.39764296 0.39732024 0.4 0.39823535] 18 ===== [0.39804845 0.39784632 0.4 0.3985964 ] 19 ===== [0.39836038 0.39825101 0.4 0.39887415] 20 ===== [0.39860033 0.39856232 0.4 0.3990878 ] 21 ===== [0.39878492 0.39880181 0.4 0.39925216] 22 ===== [0.39892691 0.39898603 0.4 0.39937859] 23 ===== [0.39903614 0.39912774 0.4 0.39947585] 24 ===== [0.39912017 0.39923676 0.4 0.39955067] 25 ===== [0.39918481 0.39932062 0.4 0.39960822] 26 ===== [0.39923453 0.39938513 0.4 0.3996525 ] 27 ===== [0.39927278 0.39943476 0.4 0.39968655] 28 ===== [0.3993022 0.39947293 0.4 0.39971275] 29 ===== [0.39932484 0.3995023 0.4 0.39973291] 30 ===== [0.39934225 0.39952489 0.4 0.39974841] 31 ===== [0.39935565 0.39954226 0.4 0.39976034] 32 ===== [0.39936595 0.39955563 0.4 0.39976951] 33 ===== [0.39937388 0.39956592 0.4 0.39977657] 34 ===== [0.39937997 0.39957383 0.4 0.399782 ] 35 ===== [0.39938466 0.39957991 0.4 0.39978618] 36 ===== [0.39938827 0.39958459 0.4 0.39978939] 37 ===== [0.39939105 0.39958819 0.4 0.39979186] 38 ===== [0.39939318 0.39959096 0.4 0.39979376] 39 ===== [0.39939482 0.3995931 0.4 0.39979522] 40 ===== [0.39939609 0.39959473 0.4 0.39979635] 41 ===== [0.39939706 0.399596 0.4 0.39979721] 42 ===== [0.39939781 0.39959697 0.4 0.39979788] 43 ===== [0.39939838 0.39959771 0.4 0.39979839] 44 ===== [0.39939882 0.39959829 0.4 0.39979879] 45 ===== [0.39939917 0.39959873 0.4 0.39979909] 46 ===== [0.39939943 0.39959907 0.4 0.39979932] 47 ===== [0.39939963 0.39959933 0.4 0.3997995 ] 48 ===== [0.39939978 0.39959953 0.4 0.39979964] 49 ===== [0.3993999 0.39959968 0.4 0.39979975] 50 ===== [0.39939999 0.3995998 0.4 0.39979983] 51 ===== [0.39940006 0.39959989 0.4 0.39979989] 52 ===== [0.39940012 0.39959997 0.4 0.39979994] 53 ===== [0.39940016 0.39960002 0.4 0.39979998] 54 ===== [0.39940019 0.39960006 0.4 0.3998 ] 55 ===== [0.39940022 0.39960009 0.4 0.39980003] 56 ===== [0.39940024 0.39960012 0.4 0.39980004] 57 ===== [0.39940025 0.39960014 0.4 0.39980006] 58 ===== [0.39940026 0.39960015 0.4 0.39980007] 59 ===== [0.39940027 0.39960016 0.4 0.39980007] 60 ===== [0.39940028 0.39960017 0.4 0.39980008] 61 ===== [0.39940028 0.39960018 0.4 0.39980008] 62 ===== [0.39940029 0.39960018 0.4 0.39980009] 63 ===== [0.39940029 0.39960019 0.4 0.39980009] 64 ===== [0.39940029 0.39960019 0.4 0.39980009] 65 ===== [0.39940029 0.39960019 0.4 0.39980009] 66 ===== [0.3994003 0.39960019 0.4 0.3998001 ] 67 ===== [0.3994003 0.3996002 0.4 0.3998001] 68 ===== [0.3994003 0.3996002 0.4 0.3998001] 69 ===== [0.3994003 0.3996002 0.4 0.3998001] 70 ===== [0.3994003 0.3996002 0.4 0.3998001] 71 ===== [0.3994003 0.3996002 0.4 0.3998001] 72 ===== [0.3994003 0.3996002 0.4 0.3998001] 73 ===== [0.3994003 0.3996002 0.4 0.3998001] 74 ===== [0.3994003 0.3996002 0.4 0.3998001] 75 ===== [0.3994003 0.3996002 0.4 0.3998001] 76 ===== [0.3994003 0.3996002 0.4 0.3998001] 77 ===== [0.3994003 0.3996002 0.4 0.3998001] 78 ===== [0.3994003 0.3996002 0.4 0.3998001] 79 ===== [0.3994003 0.3996002 0.4 0.3998001] 80 ===== [0.3994003 0.3996002 0.4 0.3998001] 81 ===== [0.3994003 0.3996002 0.4 0.3998001] 82 ===== [0.3994003 0.3996002 0.4 0.3998001] 83 ===== [0.3994003 0.3996002 0.4 0.3998001] 84 ===== [0.3994003 0.3996002 0.4 0.3998001] 85 ===== [0.3994003 0.3996002 0.4 0.3998001] 86 ===== [0.3994003 0.3996002 0.4 0.3998001] 87 ===== [0.3994003 0.3996002 0.4 0.3998001] 88 ===== [0.3994003 0.3996002 0.4 0.3998001] 89 ===== [0.3994003 0.3996002 0.4 0.3998001] 90 ===== [0.3994003 0.3996002 0.4 0.3998001] 91 ===== [0.3994003 0.3996002 0.4 0.3998001] 92 ===== [0.3994003 0.3996002 0.4 0.3998001] 93 ===== [0.3994003 0.3996002 0.4 0.3998001] 94 ===== [0.3994003 0.3996002 0.4 0.3998001] 95 ===== [0.3994003 0.3996002 0.4 0.3998001] 96 ===== [0.3994003 0.3996002 0.4 0.3998001] 97 ===== [0.3994003 0.3996002 0.4 0.3998001] 98 ===== [0.3994003 0.3996002 0.4 0.3998001] 99 ===== [0.3994003 0.3996002 0.4 0.3998001]Process finished with exit code 0

五、Graphx實現pageRank算法

import org.apache.spark.SparkConf import org.apache.spark.api.java.JavaSparkContext import org.neo4j.spark.Neo4jobject PageRank {def main(args: Array[String]): Unit = {val conf = new SparkConf().setAppName("neo4j").setMaster("local[*]").set("spark.neo4j.bolt.url","bolt://ip").set("spark.neo4j.bolt.user","user_name").set("spark.neo4j.bolt.password","passwd")val sc = new JavaSparkContext(conf)sc.setLogLevel("OFF")val nenoj = Neo4j(sc)val gpaphFrame = neo4j.pattern(("page","value"),("TO",null),("Page","value")).partitions(1).rows(100).loadGraphFrameval pageRankFrame = graphFrame.pageRank.maxIter(100).run()val ranked = pageRankFrame.verticesranked.foreach(println(_))val pageRankSort = ranked.orderBy(ranked.col("pagerank").desc)pageRankSort.foreach(println())}}

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