<p>本次主要学习图数据库中常用到的一些算法，以及如何在<code>Neo4j</code>中调用，所以这一篇偏实战，每个算法的原理就简单的提一下。</p>

1. 图数据库中常用的算法

  • PathFinding & Search

    一般用来发现Nodes之间的最短路径，常用算法有如下几种

    Google Search Results

    • Dijkstra - 边不能为负值
    • Folyd - 边可以为负值，有向图、无向图
    • Bellman-Ford
    • SPFA

  • Centrality

    一般用来计算这个图中节点的中心性，用来发现比较重要的那些Nodes。这些中心性可以有很多种，比如

    • Degree Centrality - 度中心性
    • Weighted Degree Centrality - 加权度中心性
    • Betweenness Centrality - 介数中心性
    • Closeness Centrality - 紧度中心性

  • Community Detection

    基于社区发现算法和图分析Neo4j解读《权力的游戏》

    用于发现这个图中局部联系比较紧密的Nodes，类似我们学过的聚类算法。

    • Strongly Connected Components
    • Weakly Connected Components (Union Find)
    • Label Propagation
    • Lovain Modularity
    • Triangle Count and Average Clustering Coefficient

2. 路径搜索算法

  • Shortest Path

    1
    2
    3
    4
    5
    6
    7
    		 
    MATCH (start:Loc{name:"A"}), (end:Loc{name:"F"})
    CALL algo.shortestPath.stream(start, end, "cost")
    YIELD nodeId, cost

    MATCH (other:Loc) 
    WHERE id(other) = nodeId
    RETURN other.name AS name, cost

    图数据库-Neo4j-常用算法_通用实践

  • Single Source Shortest Path

    1
    2
    3
    4
    5
    6
    		 
    MATCH (n:Loc {name:"A"})
    CALL algo.shortestPath.deltaStepping.stream(n, "cost", 3.0
    YIELD nodeId, distance

    MATCH (destination) WHERE id(destination) = nodeId
    RETURN destination.name AS destination, distance

  • All Pairs Shortest Path

    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    		 
    CALL algo.allShortestPaths.stream("cost",{nodeQuery:"Loc",defaultValue:1.0})
    YIELD sourceNodeId, targetNodeId, distance
    WITH sourceNodeId, targetNodeId, distance
    WHERE algo.isFinite(distance) = true

    MATCH (source:Loc) WHERE id(source) = sourceNodeId
    MATCH (target:Loc) WHERE id(target) = targetNodeId
    WITH source, target, distance WHERE source <> target
    RETURN source.name AS source, target.name AS target, distance
    ORDER BY distance DESC
    LIMIT 10

  • Minimum Weight Spanning Tree

    1
    2
    3
    4
    5
    		 
    MATCH (n:Place {id:"D"})
    CALL algo.spanningTree.minimum("Place", "LINK", "cost", id(n),
      {write:true, writeProperty:"MINST"})
    YIELD loadMillis, computeMillis, writeMillis, effectiveNodeCount
    RETURN loadMillis, computeMillis, writeMillis, effectiveNodeCount;

  • CASE

    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    		 
    MERGE (a:Loc {name:"A"})
    MERGE (b:Loc {name:"B"})
    MERGE (c:Loc {name:"C"})
    MERGE (d:Loc {name:"D"})
    MERGE (e:Loc {name:"E"})
    MERGE (f:Loc {name:"F"})
    MERGE (a)-[:ROAD {cost:50}]->(b)
    MERGE (a)-[:ROAD {cost:50}]->(c)
    MERGE (a)-[:ROAD {cost:100}]->(d)
    MERGE (b)-[:ROAD {cost:40}]->(d)
    MERGE (c)-[:ROAD {cost:40}]->(d)
    MERGE (c)-[:ROAD {cost:80}]->(e)
    MERGE (d)-[:ROAD {cost:30}]->(e)
    MERGE (d)-[:ROAD {cost:80}]->(f)
    MERGE (e)-[:ROAD {cost:40}]->(f);

3. 中心性算法

  • PageRank

    1
    2
    3
    4
    5
    6
    		 
    CALL algo.pageRank.stream("Page", "LINKS",
    {iterations:20})
    YIELD nodeId, score
    MATCH (node) WHERE id(node) = nodeId
    RETURN node.name AS page,score
    ORDER BY score DESC

    图数据库-Neo4j-常用算法_java经验集锦_02

  • Degree Centrality

  • Betweenness Centrality

    1
    2
    3
    4
    5
    		 
    CALL algo.betweenness.stream("User", "MANAGES", {direction:"out"})
    YIELD nodeId, centrality
    MATCH (user:User) WHERE id(user) = nodeId
    RETURN user.id AS user,centrality
    ORDER BY centrality DESC;

  • Closeness Centrality

    1
    2
    3
    4
    5
    6
    		 
    CALL algo.closeness.stream("Node", "LINK")
    YIELD nodeId, centrality
    MATCH (n:Node) WHERE id(n) = nodeId
    RETURN n.id AS node, centrality
    ORDER BY centrality DESC
    LIMIT 20;

  • CASE

    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    		 
    MERGE (home:Page {name:"Home"})
    MERGE (about:Page {name:"About"})
    MERGE (product:Page {name:"Product"})
    MERGE (links:Page {name:"Links"})
    MERGE (a:Page {name:"Site A"})
    MERGE (b:Page {name:"Site B"})
    MERGE (c:Page {name:"Site C"})
    MERGE (d:Page {name:"Site D"})
    MERGE (home)-[:LINKS]->(about)
    MERGE (about)-[:LINKS]->(home)
    MERGE (product)-[:LINKS]->(home)
    MERGE (home)-[:LINKS]->(product)
    MERGE (links)-[:LINKS]->(home)
    MERGE (home)-[:LINKS]->(links)
    MERGE (links)-[:LINKS]->(a)
    MERGE (a)-[:LINKS]->(home)
    MERGE (links)-[:LINKS]->(b)
    MERGE (b)-[:LINKS]->(home)
    MERGE (links)-[:LINKS]->(c)
    MERGE (c)-[:LINKS]->(home)
    MERGE (links)-[:LINKS]->(d)
    MERGE (d)-[:LINKS]->(home)

4. 社区发现算法

  • Strongly Connected Components

    1
    2
    3
    4
    		 
    CALL algo.scc.stream("User","FOLLOWS")
    YIELD nodeId, partition
    MATCH (u:User) WHERE id(u) = nodeId
    RETURN u.id AS name, partition

  • Weakly Connected Components (Union Find)

    1
    2
    3
    4
    		 
    CALL algo.unionFind.stream("User", "FRIEND", {})
    YIELD nodeId,setId
    MATCH (u:User) WHERE id(u) = nodeId
    RETURN u.id AS user, setId

  • Label Propagation

    1
    2
    		 
    CALL algo.labelPropagation.stream("User", "FOLLOWS",
     {direction: "OUTGOING", iterations: 10})

  • Lovain Modularity

    1
    2
    3
    4
    5
    		 
    CALL algo.louvain.stream("User", "FRIEND", {})
    YIELD nodeId, community
    MATCH (user:User) WHERE id(user) = nodeId
    RETURN user.id AS user, community
    ORDER BY community;

  • Triangle Count and Average Clustering Coefficient

    1
    2
    3
    4
    5
    6
    		 
    CALL algo.triangle.stream("Person","KNOWS")
    YIELD nodeA,nodeB,nodeC
    MATCH (a:Person) WHERE id(a) = nodeA
    MATCH (b:Person) WHERE id(b) = nodeB
    MATCH (c:Person) WHERE id(c) = nodeC
    RETURN a.id AS nodeA, b.id AS nodeB, c.id AS node

5. References

  • Neo4j in deep
  • 官方文档：Comprehensive-Guide-to-Graph-Algorithms-in-Neo4j-ebook
  原文地址：https://chenson.cc/2018/08/18/%E5%9B%BE%E6%95%B0%E6%8D%AE%E5%BA%93-Neo4j-%E5%B8%B8%E7%94%A8%E7%AE%97%E6%B3%95/
</div>