Overview

K-Hop Whole Graph algorithm calculates the number of K-hop neighbors for each node and returns those neighbors. The algorithm is widely used in scenarios such as relationship discovery, impact prediction and friend suggestion and so on.

K-Hop Whole Graph can be viewed as the batch execution of UQL command khop(). Although Ultipa has optimized the K-Hop Whole Graph algorithm for high concurrency performance, massive system resources can still be consumed by the algorithm in large graphs (over tens of millions nodes and edges) or graphs with many super nodes. Therefore, it is recommended to avoid performing K-Hop Whole Graph calculation that is too deep.

In a graph which nodes/edges = 100, the theoretical computation amount required to query 5-hop neighbors of a node is 10⁵ (10 billion computational complexity) and it would take 100ms; then 1 million seconds (12 days) are needed to complete such query in a graph of 10 million nodes.

Basic Concept

BFS

BFS is short for Breadth First Search, together with DFS (Depth First Search), are two the most basic traversal principles. K-Hop query follows BFS principle, which means that when traversing the whole graph from one node, it first traverses all the neighbor nodes of the current node that have not arrived yet, and then traverses the neighbor nodes of these neighbor nodes in turns that have not arrived yet.

Starting from the red node and traversing by the BFS principle, the yellow, green, blue nodes are found in succession. Color of these nodes is classified by the distance to the start node, that is, the number of edges of the shortest path(s) from the start node to them. This distance is what the K means in K-Hop query, which is the K-hop neighbors of the start node.

Once the start node is given, K values of the other nodes in the graph are also determined. In other words, if a node is the 5th level neighbor of the start node, then it is impossible to appear in the 4th, 6th or other levels.

Direction of K-Hop

K-Hop query in directed graph can be restrained by the direction of the edge where the neighbor is located, this is when some nodes do not have K values and not all nodes are found in the traversal result.

Starting from the red node in the directed graph on the left side, and traversing by the outbound edges and inbound edges; two distinct traversal results are obtained, the purple node does not belong to any level when traversing in the inbound direction and its K value does not exist.

Special Case

Lonely Node, Disconnected Graph

Lonely node will not appear in any K-Hop query result.

For disconnected graph, only nodes belong to the same connected component with the start node are involved in the K-Hop query result, while other nodes cannot be traversed.

Self-loop Edge

Each node is traversed only once in K-Hop query, so the self-loop edge of node can be considered invalid.

Directed Edge

When the K-Hop query is performed without specifying the direction of edges, the direction of edges is ignored, and certain K values are calculated for all nodes in the connected component where that start node is located.

Results and Statistics

Take the transaction graph below as an example, the color of card represent its level, run the K-Hop Whole Graph algorithm against all nodes:

Algorithm results: Calculate 1-hop neighbors for each node and count the maximum level of the results, return _id, value or _uuid, value according to the execution method, column value includes the aggregative counting result(s) and the number of neighbors

Algorithm statistics: N/A

Command and Configuration

• Command: algo(khop_all)
• Configurations for the parameter params():

Example: Calculate the number of 2-hop neighbors in the outbound direction of all nodes

algo(khop_all).params({ 
  k_start: 2,
  k_end: 2,
  direction: "out"
}) as k2
return k2

Example: Calculate 2-hop and 3-hop neighbors of nodes UUID = 3,4,5 and aggregatively count the maximum value of property @card.level and sum of property @card.balance of the results, also include the start node (UUID = 3,4,5) in each node's results

algo(khop_all).params({ 
  uuids: [3,4,5],
  k_start: 2,
  k_end: 3,
  src_include: 1,
  node_property: [@card.level, @card.balance],
  aggregate_opt: ["max", "sum"]
}) as k2
return k2

Algorithm Execution

Task Writeback

1. File Writeback

Example: Calculate 2-hop and 3-hop neighbors of all nodes and aggregatively count the maximum value of property @card.level and sum of property @card.balance of the results, write the IDs of neighbors of each node back to file named neighbors, write the aggregative counting results and the number of neighbors of each node back to file named counts

algo(khop_all).params({ 
  k_start: 3,
  k_end: 3,
  node_property: [@card.level, @card.balance],
  aggregate_opt: ["max", "sum"]
}).write({
  file:{
    filename_ids: "neighbors",
    filename: "counts"
  }
})

2. Property Writeback

Example: Calculate 2-hop neighbors of all nodes, write the number of neighbors back to node property named khop2

algo(khop_all).params({ 
  k_start: 2,
  k_end: 2
}).write({
  db:{ 
    property: "khop2"
  }
})

3. Statistics Writeback

This algorithm has no statistics.

Direct Return

Example: Calculate 3-hop neighbors of all nodes and aggregatively count the maximum value of property @card.level and sum of property @card.balance of the results, define algorithm results as alias named nei, and return the results

algo(khop_all).params({ 
  k_start: 3,
  k_end: 3,
  node_property: [@card.level, @card.balance],
  aggregate_opt: ["max", "sum"]
}) as nei
return nei

Streaming Return

Example: Calculate 1-hop to 3-hop neighbors of node UUID = 3 and aggregatively count the maximum value of property @card.level of the results, and return only the aggregative counting result and the number of neighbors

algo(khop_all).params({
   uuids: [3],
   k_start: 1,
   k_end: 3,
   node_property: @card.level,
   aggregate_opt: max
}).stream() as results 
return results.value

Real-time Statistics

This algorithm has no statistics.