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‎built-in-algorithms/md/pgx_builtin_a1_prim.md‎

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- **Time Complexity:** O(E + V log V) with V = number of vertices, E = number of edges
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- **Space Requirement:** O(2 * E + V) with V = number of vertices, E = number of edges
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- **Javadoc:**
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- [Analyst#prim(PgxGraph graph, EdgeProperty<java.lang.Double> weight)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_)
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- [Analyst#prim(PgxGraph graph, EdgeProperty<java.lang.Double> weight, EdgeProperty<java.lang.Boolean> mst)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_oracle_pgx_api_EdgeProperty_)
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- [Analyst#prim(PgxGraph graph, EdgeProperty<java.lang.Double> weight)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_)
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- [Analyst#prim(PgxGraph graph, EdgeProperty<java.lang.Double> weight, EdgeProperty<java.lang.Boolean> mst)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_oracle_pgx_api_EdgeProperty_)
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This implementation of Prim's algorithm works on undirected graphs that are connected and have no multi-edges (i.e. more than one edge connecting the same pair of vertices). The algorithm computes the minimum spanning tree (MST) of the graph using the weights associated to each edge. A minimum spanning tree is a subset of the edges that connects all the vertices in the graph such that it minimizes the total weight associated to the edges.
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```java
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/*
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* Copyright (C) 2013 - 2024 Oracle and/or its affiliates. All rights reserved.
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* Copyright (C) 2013 - 2025 Oracle and/or its affiliates. All rights reserved.
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*/
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package oracle.pgx.algorithms;
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‎built-in-algorithms/md/pgx_builtin_a1u_prim.md‎

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- **Time Complexity:** O(E + V log V) with V = number of vertices, E = number of edges
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- **Space Requirement:** O(2 * E + V) with V = number of vertices, E = number of edges
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- **Javadoc:**
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- [Analyst#prim(PgxGraph graph, EdgeProperty weight)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_)
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- [Analyst#prim(PgxGraph graph, EdgeProperty weight, EdgeProperty mst)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_oracle_pgx_api_EdgeProperty_)
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- [Analyst#prim(PgxGraph graph, EdgeProperty weight)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_)
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- [Analyst#prim(PgxGraph graph, EdgeProperty weight, EdgeProperty mst)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#prim_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_oracle_pgx_api_EdgeProperty_)
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This implementation of Prim's algorithm works on directed graphs that are connected but ignores edge directions to interpret the graph as undirected. The algorithm computes the minimum spanning tree (MST) of the graph using the weights associated to each edge. A minimum spanning tree is a subset of the edges that connects all the vertices in the graph such that it minimizes the total weight associated to the edges.
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```java
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/*
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* Copyright (C) 2013 - 2024 Oracle and/or its affiliates. All rights reserved.
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* Copyright (C) 2013 - 2025 Oracle and/or its affiliates. All rights reserved.
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*/
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package oracle.pgx.algorithms;
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‎built-in-algorithms/md/pgx_builtin_c1_community_detection_label_propagation.md‎

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- **Time Complexity:** O(E * k) with E = number of edges, k <= maximum number of iterations
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- **Space Requirement:** O(2 * V) with V = number of vertices
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- **Javadoc:**
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- [Analyst#communitiesLabelPropagation(PgxGraph graph)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph, int maxIterations)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_int_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph, int maxIterations, VertexProperty<ID,java.lang.Long> partitionDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_int_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph, VertexProperty<ID,java.lang.Long> partitionDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph, int maxIterations)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_int_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph, int maxIterations, VertexProperty<ID,java.lang.Long> partitionDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_int_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesLabelPropagation(PgxGraph graph, VertexProperty<ID,java.lang.Long> partitionDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesLabelPropagation_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_)
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Label Propagation is an algorithm designed to find community structures in a graph. It assigns a unique community label to each vertex in the graph, which then is updated on each iteration by looking and choosing the most frequent label amongst those from its neighbors. Convergence is achieved once the label of each vertex is the same as the most frequent one amongst its neighbors, i.e. when there are no changes in the communities assigned to the vertices in one iteration.
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```java
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/*
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* Copyright (C) 2013 - 2024 Oracle and/or its affiliates. All rights reserved.
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* Copyright (C) 2013 - 2025 Oracle and/or its affiliates. All rights reserved.
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*/
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package oracle.pgx.algorithms;
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‎built-in-algorithms/md/pgx_builtin_c2_community_detection_conductance_minimization.md‎

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- **Time Complexity:** O(E * k) with E = number of edges, k <= maximum number of iterations
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- **Space Requirement:** O(5 * V + 2 * E) with V = number of vertices, E = number of edges
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- **Javadoc:**
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph, int max)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_int_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph, int max, VertexProperty<ID,java.lang.Long> partitonDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_int_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph, VertexProperty<ID,java.lang.Long> partitonDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph, int max)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_int_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph, int max, VertexProperty<ID,java.lang.Long> partitonDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_int_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesConductanceMinimization(PgxGraph graph, VertexProperty<ID,java.lang.Long> partitonDistribution)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesConductanceMinimization_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_)
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The algorithm proposed by Soman and Narang to find community structures in a graph can be regarded as a variant of the label propagation algorithm, since it takes into account weights over the edges when looking for the community assignments. This implementation generates the weight of the edges by using the triangles in the graph, and just like label propagation, it assigns a unique community label to each vertex in the graph at the beginning, which is then updated on each iteration by looking and choosing the most frequent label from the labels of their neighbors. Convergence is achieved once the label of each vertex is the same as the most frequent one amongst its neighbors, i.e. when there are no changes in the communities assigned to the vertices in one iteration.
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```java
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/*
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* Copyright (C) 2013 - 2024 Oracle and/or its affiliates. All rights reserved.
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* Copyright (C) 2013 - 2025 Oracle and/or its affiliates. All rights reserved.
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*/
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package oracle.pgx.algorithms;
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‎built-in-algorithms/md/pgx_builtin_c3_infomap.md‎

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- **Time Complexity:** O((k ^ 2) * E) with E = number of edges, k <= maximum number of iterations
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- **Space Requirement:** O(10 * V + 2 * E) with V = number of vertices, E = number of edges
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- **Javadoc:**
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight, double tau, double tol, int maxIter)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_double_double_int_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight, double tau, double tol, int maxIter, VertexProperty<ID,java.lang.Long> module)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_double_double_int_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight, VertexProperty<ID,java.lang.Long> module)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight, double tau, double tol, int maxIter)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_double_double_int_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight, double tau, double tol, int maxIter, VertexProperty<ID,java.lang.Long> module)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_double_double_int_oracle_pgx_api_VertexProperty_)
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- [Analyst#communitiesInfomap(PgxGraph graph, VertexProperty<ID,java.lang.Double> rank, EdgeProperty<java.lang.Double> weight, VertexProperty<ID,java.lang.Long> module)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#communitiesInfomap_oracle_pgx_api_PgxGraph_oracle_pgx_api_VertexProperty_oracle_pgx_api_EdgeProperty_oracle_pgx_api_VertexProperty_)
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Infomap is a robust algorithm designed to find community structures in a graph that requires some pre-processing steps. This implementation needs a reciprocated or an undirected graph, as well as the ranking score from the normalized weighted version of the Pagerank algorithm. It will assign a unique module (or community) label to each vertex in the graph based on their Pagerank score, edge weights and the labels of their neighbors. It is an iterative algorithm that updates the labels of the vertices in random order on each iteration using the previous factors, converging once there are no further changes in the vertex labels, or once the maximum number of iterations is reached. The algorithm is non-deterministic because of the random order for visiting and updating the vertex labels, thus the communities found might be different each time the algorithm is run.
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```java
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/*
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* Copyright (C) 2013 - 2024 Oracle and/or its affiliates. All rights reserved.
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* Copyright (C) 2013 - 2025 Oracle and/or its affiliates. All rights reserved.
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*/
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package oracle.pgx.algorithms;
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‎built-in-algorithms/md/pgx_builtin_c4_louvain.md‎

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- **Time Complexity:** O(E * k) with E = number of edges, k <= maximum number of iterations
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- **Space Requirement:** O(8 * V + E) with V = number of vertices
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- **Javadoc:**
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- [Analyst#louvain(PgxGraph graph, EdgeProperty<java.lang.Double> weight)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#louvain_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_)
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- [Analyst#louvain(PgxGraph graph, EdgeProperty<java.lang.Double> weight, int maxIter)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#louvain_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_int_)
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- [Analyst#louvain(PgxGraph graph, EdgeProperty<java.lang.Double> weight, int maxIter, int nbrPass, double tol, VertexProperty<ID,java.lang.Long> community)](https://docs.oracle.com/en/database/oracle/property-graph/24.4/spgjv/oracle/pgx/api/Analyst.html#louvain_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_int_int_double_oracle_pgx_api_VertexProperty_)
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- [Analyst#louvain(PgxGraph graph, EdgeProperty<java.lang.Double> weight)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#louvain_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_)
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- [Analyst#louvain(PgxGraph graph, EdgeProperty<java.lang.Double> weight, int maxIter)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#louvain_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_int_)
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- [Analyst#louvain(PgxGraph graph, EdgeProperty<java.lang.Double> weight, int maxIter, int nbrPass, double tol, VertexProperty<ID,java.lang.Long> community)](https://docs.oracle.com/en/database/oracle/property-graph/25.1/spgjv/oracle/pgx/api/Analyst.html#louvain_oracle_pgx_api_PgxGraph_oracle_pgx_api_EdgeProperty_int_int_double_oracle_pgx_api_VertexProperty_)
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Louvain is an algorithm for community detection in large graphs which uses the graph's modularity. Initially it assigns a different community to each node of the graph. It then iterates over the nodes and evaluates for each node the modularity gain obtained by removing the node from its community and placing it in the community of one of its neighbors. The node is placed in the community for which the modularity gain is maximum. This process is repeated for all nodes until no improvement is possible, i.e until no new assignment of a node to a different community can improve the graph's modularity.
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```java
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/*
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* Copyright (C) 2013 - 2024 Oracle and/or its affiliates. All rights reserved.
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* Copyright (C) 2013 - 2025 Oracle and/or its affiliates. All rights reserved.
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*/
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package oracle.pgx.algorithms;
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