Vertex Clustering Coefficient - Platform For AI - Alibaba Cloud Documentation Center

A vertex clustering coefficient is a measure of the degree to which vertices in an undirected graph tend to cluster together, which indicates the density. You can use the vertex clustering coefficient to compare the densities of different groups and estimate the maximum density of a group. The Vertex Clustering Coefficient component can provide the number of neighboring vertices, the density, and the number of pairs of neighbors.

Algorithm description

A vertex clustering coefficient is used to calculate the peripheral density of a vertex in an undirected graph. The density of a star network is 0, and that of a fully meshed network is 1.

Configure the component

Method 1: Configure the component on the pipeline page

You can add the Vertex Clustering Coefficient component on the pipeline page of Machine Learning Designer in the Platform for AI (PAI) console. The following table describes the parameters.

Tab	Parameter	Description
Fields Setting	Start Vertex	The start vertex column in the edge table.
Fields Setting	End Vertex	The end vertex column in the edge table.
Parameters Setting	Largest Vertex Degree	If the vertex degree is larger than the value of this parameter, sampling is required. Default value: 500.
Tuning	Workers	The number of vertices for parallel job execution. The degree of parallelism and framework communication costs increase with the value of this parameter.
	Memory Size per Worker (MB)	The maximum size of memory that a single job can use. Unit: MB. Default value: 4096. If the size of used memory exceeds the value of this parameter, the `OutOfMemory` error is reported.
	Data Split Size (MB)	The data split size. Unit: MB. Default value: 64.

Method 2: Configure the component by using PAI commands

You can configure the Vertex Clustering Coefficient component by using PAI commands. You can use the SQL Script component to run PAI commands. For more information, see Scenario 4: Execute PAI commands within the SQL script component in the "SQL Script" topic.

PAI -name NodeDensity
    -project algo_public
    -DinputEdgeTableName=NodeDensity_func_test_edge
    -DfromVertexCol=flow_out_id
    -DtoVertexCol=flow_in_id
    -DoutputTableName=NodeDensity_func_test_result
    -DmaxEdgeCnt=500;

Parameter	Required	Default value	Description
inputEdgeTableName	Yes	No default value	The name of the input edge table.
inputEdgeTablePartitions	No	Full table	The partitions in the input edge table.
fromVertexCol	Yes	No default value	The start vertex column in the input edge table.
toVertexCol	Yes	No default value	The end vertex column in the input edge table.
outputTableName	Yes	No default value	The name of the output table.
outputTablePartitions	No	No default value	The partitions in the output table.
lifecycle	No	No default value	The lifecycle of the output table.
maxEdgeCnt	No	500	If the vertex degree is greater than the value of this parameter, sampling is required.
workerNum	No	No default value	The number of vertices for parallel job execution. The degree of parallelism and framework communication costs increase with the value of this parameter.
workerMem	No	4096	The maximum size of memory that a single job can use. Unit: MB. Default value: 4096. If the size of used memory exceeds the value of this parameter, the `OutOfMemory` error is reported.
splitSize	No	64	The data split size. Unit: MB.

Example

Add the SQL Script component as a vertex to the canvas and execute the following SQL statements to generate training data.

drop table if exists NodeDensity_func_test_edge;
create table NodeDensity_func_test_edge as
select * from
(
  select '1' as flow_out_id, '2' as flow_in_id
  union all
  select '1' as flow_out_id, '3' as flow_in_id
  union all
  select '1' as flow_out_id, '4' as flow_in_id
  union all
  select '1' as flow_out_id, '5' as flow_in_id
  union all
  select '1' as flow_out_id, '6' as flow_in_id
  union all
  select '2' as flow_out_id, '3' as flow_in_id
  union all
  select '3' as flow_out_id, '4' as flow_in_id
  union all
  select '4' as flow_out_id, '5' as flow_in_id
  union all
  select '5' as flow_out_id, '6' as flow_in_id
  union all
  select '5' as flow_out_id, '7' as flow_in_id
  union all
  select '6' as flow_out_id, '7' as flow_in_id
)tmp;
drop table if exists NodeDensity_func_test_result;
create table NodeDensity_func_test_result
(
  node string,
  node_cnt bigint,
  edge_cnt bigint,
  density double,
  log_density double
);

Data structure

Add the SQL Script component as a vertex to the canvas and run the following PAI commands to train the model.

drop table if exists ${o1};
PAI -name NodeDensity
    -project algo_public
    -DinputEdgeTableName=NodeDensity_func_test_edge
    -DfromVertexCol=flow_out_id
    -DtoVertexCol=flow_in_id
    -DoutputTableName=${o1}
    -DmaxEdgeCnt=500;

Right-click the SQL Script component and choose View Data > SQL Script Output to view the training results.

| node | node_cnt | edge_cnt | density | log_density |
| ---- | -------- | -------- | ------- | ----------- |
| 1    | 5        | 4        | 0.4     | 1.45657     |
| 2    | 2        | 1        | 1.0     | 1.24696     |
| 3    | 3        | 2        | 0.66667 | 1.35204     |
| 4    | 3        | 2        | 0.66667 | 1.35204     |
| 5    | 4        | 3        | 0.5     | 1.41189     |
| 6    | 3        | 2        | 0.66667 | 1.35204     |
| 7    | 2        | 1        | 1.0     | 1.24696     |