Leiden-refine optimization algorithm based on union-find algorithm
View Patent ↗A computer-implemented method includes: receiving data encoding an input graph comprising a group of nodes and a group of edges each connecting two nodes from the group of nodes, wherein each node represents a user on a platform with a group of users clustered into an initial set of communities; partitioning the input graph into a set of subgraphs each comprising more than one partitioned community of users; processing each subgraph using a Union-Find algorithm to generate a processed subgraph showing a revised community with a 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 set of fine-grained communities; and merging the set of fine-grained communities to construct an output graph showing the plurality of users clustered into a new set of communities.
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.