Leiden-refine optimization algorithm based on union-find algorithm

1 . A computer-implemented method comprising:

receiving data encoding an input graph comprising a plurality of nodes and a plurality of edges, each edge connecting two nodes from the plurality of nodes, wherein each node represents a user on an online platform with a plurality of users;

partitioning the input graph into a plurality of subgraphs each comprising more than one partitioned community of users;

processing each subgraph using a Union-Find algorithm to generate a processed subgraph representing a revised community with an intra-community connectivity metric higher than the more than one partitioned community of users;

processing each processed subgraph to split the revised community into a plurality of fine-grained communities; and

merging the plurality of fine-grained communities to construct an output graph representing the plurality of users on the online platform clustered into a set of detected communities.

2 . The computer-implemented method of claim 1 , wherein processing each subgraph using a Union-Find algorithm comprises:

decomposing a subgraph to recast each node of the subgraph as an individual community.

3 . The computer-implemented method of claim 2 , further comprising:

traversing each edge of the subgraph to merge two individual communities connected by the corresponding edge when the two individual communities are different; and

organizing the merged individual communities to generate the processed subgraph.

4 . The computer-implemented method of claim 3 , wherein each individual community has a community number determined by a corresponding node, and

wherein when the two individual communities are merged into a new community, the new community has a community number determined by a smaller community number of the two individual communities.

5 . The computer-implemented method of claim 3 , wherein nodes inside the processed subgraph with identical community numbers form one community.

6 . The computer-implemented method of claim 1 , wherein the intra-community connectivity metric comprises at least one of: a metric for density of connections, a metric for connected component, a metric for internal cohesion, and a metric for modularity contribution.

7 . The computer-implemented method of claim 6 , further comprising:

in response to determining that the intra-community connectivity metric has not reached a threshold level, re-partitioning the output graph into a plurality of new subgraphs for continued processing.

8 . One or more non-transitory, computer-readable storage media encoded with instructions that, when executed by one or more computers, cause the one or more computers to perform operations comprising:

receiving data encoding an input graph comprising a plurality of nodes and a plurality of edges each connecting two nodes from the plurality of nodes, wherein each node represents a user on an online platform with a plurality of users;

partitioning the input graph into a plurality of subgraphs each comprising more than one partitioned community of users;

processing each subgraph using a Union-Find algorithm to generate a processed subgraph representing a revised community with an intra-community connectivity metric higher than the more than one partitioned community of users;

processing each processed subgraph to split the revised community into a plurality of fine-grained communities; and

merging the plurality of fine-grained communities to construct an output graph representing the plurality of users on the online platform clustered into a set of detected communities.

9 . The one or more non-transitory, computer-readable storage media of claim 8 , wherein processing each subgraph using a Union-Find algorithm comprises:

decomposing a subgraph to recast each node of the subgraph as an individual community.

10 . The one or more non-transitory, computer-readable storage media of claim 9 , wherein the operations further comprise:

traversing each edge of the subgraph to merge two individual communities connected by the corresponding edge when the two individual communities are different; and

organizing the merged individual communities to generate the processed subgraph.

11 . The one or more non-transitory, computer-readable storage media of claim 10 , wherein each individual community has a community number determined by a corresponding node, and

wherein when the two individual communities are merged into a new community, the new community has a community number determined by a smaller community number of the two individual communities.

12 . The one or more non-transitory, computer-readable storage media of claim 10 , wherein nodes inside the processed subgraph with identical community numbers form one community.

13 . The one or more non-transitory, computer-readable storage media of claim 8 , wherein the intra-community connectivity metric comprises at least one of: a metric for density of connections, a metric for connected component, a metric for internal cohesion, and a metric for modularity contribution.

14 . The one or more non-transitory, computer-readable storage media of claim 13 , wherein the operations further comprise:

in response to determining that the intra-community connectivity metric has not reached a threshold level, re-partitioning the output graph into a plurality of new subgraphs for continued processing.

15 . A computer system comprising one or more computer processors configured to perform operations comprising:

receiving data encoding an input graph comprising a plurality of nodes and a plurality of edges each connecting two nodes from the plurality of nodes, wherein each node represents a user on an online platform with a plurality of users;

partitioning the input graph into a plurality of subgraphs each comprising more than one partitioned community of users;

processing each subgraph using a Union-Find algorithm to generate a processed subgraph representing a revised community with an intra-community connectivity metric higher than the more than one partitioned community of users;

processing each processed subgraph to split the revised community into a plurality of fine-grained communities; and

merging the plurality of fine-grained communities to construct an output graph representing the plurality of users on the online platform clustered into a set of detected communities.

16 . The computer system of claim 15 , wherein processing each subgraph using a Union-Find algorithm comprises:

decomposing a subgraph to recast each node of the subgraph as an individual community.

17 . The computer system of claim 16 , wherein the operations further comprise:

traversing each edge of the subgraph to merge two individual communities connected by the corresponding edge when the two individual communities are different; and

organizing the merged individual communities to generate the processed subgraph.

18 . The computer system of claim 17 , wherein each individual community has a community number determined by a corresponding node, and

wherein when the two individual communities are merged into a new community, the new community has a community number determined by a smaller community number of the two individual communities.

19 . The computer system of claim 15 , wherein nodes inside the processed subgraph with identical community numbers form one community.

20 . The computer system of claim 15 , wherein the intra-community connectivity metric comprises at least one of: a metric for density of connections, a metric for connected component, a metric for internal cohesion, and a metric for modularity contribution, and

wherein the operations further comprise: in response to determining that the intra-community connectivity metric has not reached a threshold level, re-partitioning the output graph into a plurality of new subgraphs for continued processing.