k-Core Decomposition
A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least \$k\$ vertices in the subgraph.
This algorithm takes a range of values for \$k\$ and returns the vertex set that constitutes the k-core with the highest possible value of \$k\$ within the range.
To obtain the k-core of a graph, the algorithm first deletes the vertices whose outdegree is less than k. It then updates the outdegree of the neighbors of the deleted vertices, and if that causes a vertex’s outdegree to fall below k, it will also delete that vertex. The algorithm repeats this operation until every vertex left in the subgraph has an outdegree of at least k.
Notes
This is an implementation of Algorithm 2 in Scalable K-Core Decomposition for Static Graphs Using a Dynamic Graph Data Structure, Tripathy et al., IEEE Big Data 2018.
Specifications
tg_kcore(STRING v_type, STRING e_type, INT k_min = 0,
INT k_max = -1, BOOL print_results = TRUE,
STRING result_attribute = "", STRING file_path = "",
BOOL print_all_k = FALSE, BOOL show_shells=FALSE)
Parameters
Parameter | Description |
---|---|
|
Vertex type to include in the k-core |
|
Edge type to count for k-core connections |
|
Minimum value of k. If the actual maximum core is below |
|
Maximum value of k. If |
|
Boolean value that decides whether the algorithm will return output in JSON |
|
An attribute of the vertex to save the core level of the vertex to. If |
|
If |
|
Whether to print all k connections |
|
The k-shell is the set of vertices that are part of the k-core but not part of the (k+1)-core. If |
Example
In the example below based on the social
graph from GSQL 101, we can see that Dan, Tom, and Jenny make up a 2-core, which is the max-core of the graph:
If we run the kcore
algorithm on this small graph like so:
RUN QUERY tg_kcore("person", "friendship", 0, -1, TRUE, "", "", FALSE, FALSE)
Here is the returned JSON response, which includes a 2-core that is comprised of Dan, Jenny, and Tom:
[
{
"core_size": 3,
"k": 2, // the k-core with the highest possible k is returned
"max_core": [
{
"attributes": {
"@core": 2,
"@deg": 0,
"age": 40,
"gender": "male",
"name": "Tom",
"state": "ca"
},
"v_id": "Tom",
"v_type": "person"
},
{
"attributes": {
"@core": 2,
"@deg": 0,
"age": 34,
"gender": "male",
"name": "Dan",
"state": "ny"
},
"v_id": "Dan",
"v_type": "person"
},
{
"attributes": {
"@core": 2,
"@deg": 0,
"age": 25,
"gender": "female",
"name": "Jenny",
"state": "tx"
},
"v_id": "Jenny",
"v_type": "person"
}
]
}
]