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# Network Community Detection and Visualization
This repository provides a set of functions to perform community detection on networks using algorithms like Girvan-Newman and Louvain. Additionally, it includes utilities to calculate modularity and visualize the detected communities with various layouts.
## Functions Overview
### 1. `calculate_modularity(G, partition)`
This function calculates the modularity of a given partition of a graph `G`. Modularity is a measure of the strength of division of a network into communities.
- **Parameters**:
- `G` (networkx.Graph): The input graph.
- `partition` (list of sets or dict): The partition of the graph where each set (or dict) represents a community.
- **Returns**:
- `float`: The modularity score.
### 2. `get_modularity(G, partition)`
This function calculates the modularity of the current partition using an alternative method based on node degrees and community assignments.
- **Parameters**:
- `G` (networkx.Graph): The graph for which modularity is to be calculated.
- `partition` (dict): A dictionary where keys are nodes and values are community labels.
- **Returns**:
- `float`: The modularity score.
### 3. `local_optimization_step(H, Q_max)`
This function performs a local optimization step on the graph to maximize modularity by moving nodes to neighboring communities.
- **Parameters**:
- `H` (networkx.Graph): The graph with community assignments as node attributes.
- `Q_max` (float): The current maximum modularity.
- **Returns**:
- `float`: The updated maximum modularity after the optimization step.
### 4. `network_aggregation_step(H)`
This function performs the network aggregation step by collapsing communities into super-nodes and recalculating edge weights between communities.
- **Parameters**:
- `H` (networkx.Graph): The graph where each node has a 'community' attribute.
- **Returns**:
- `networkx.Graph`: A new graph where nodes represent communities from the previous step.
### 5. `reindex_communities(partition)`
This function reindexes the communities in the partition so that community labels are continuous.
- **Parameters**:
- `partition` (dict): A dictionary where keys are nodes and values are community labels.
- **Returns**:
- `dict`: A new partition where community labels are reindexed.
### 6. `louvain_method(G, init=None)`
This function runs the Louvain method for community detection on a graph.
- **Parameters**:
- `G` (networkx.Graph): The input graph where nodes and edges define the structure.
- `init` (dict): Optional initial partition.
- **Returns**:
- `dict`: The final partition of the graph with node assignments to communities.
### 7. `vis_network_spring(G, best_partition, layout_type="spring_layout")`
This function visualizes a network with a specified layout, coloring nodes by community.
- **Parameters**:
- `G` (networkx.Graph): The graph to visualize.
- `best_partition` (dict): A partition of the graph nodes (community assignments).
- `layout_type` (str): The layout algorithm to use. Options are "spring_layout", "shell_layout", and "kamada_kawai_layout".
- **Returns**:
- `None`: Displays the network graph.
### 8. `vis_network_agg_spring(G, best_partition, layout1="shell_layout", iterations=1)`
This function visualizes a network using an aggregated layout approach. The first layout is either 'shell_layout' or 'kamada_kawai_layout', and the second layout is always 'spring_layout' for a specified number of iterations.
- **Parameters**:
- `G` (networkx.Graph): The graph to visualize.
- `best_partition` (dict): A partition of the graph nodes (community assignments).
- `layout1` (str): The first layout algorithm to use, either 'shell_layout' or 'kamada_kawai_layout'.
- `iterations` (int): The number of iterations for the 'spring_layout' adjustment.
- **Returns**:
- `None`: Displays the network graph.
### 9. `vis_network_partition_process(G, pos=None, method="girvan_newman", w=5.0, h=4.0, nrows=6, ncols=6, iterations_limit=None)`
This function visualizes the partitioning process of a network using the Girvan-Newman algorithm.
- **Parameters**:
- `G` (networkx.Graph): The input graph.
- `pos` (dict or None): Positions for the nodes in the graph. If None, default spring_layout will be used.
- `method` (str): Only "girvan_newman" is supported.
- `w` (float): Width of each subplot.
- `h` (float): Height of each subplot.
- `nrows` (int): Number of rows in the grid of subplots.
- `ncols` (int): Number of columns in the grid of subplots.
- `iterations_limit` (int): Limit the number of iterations to display.
- **Returns**:
- `None`: Displays the partitioning process.
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"description": "# Network Community Detection and Visualization\n\nThis repository provides a set of functions to perform community detection on networks using algorithms like Girvan-Newman and Louvain. Additionally, it includes utilities to calculate modularity and visualize the detected communities with various layouts.\n\n## Functions Overview\n\n### 1. `calculate_modularity(G, partition)`\nThis function calculates the modularity of a given partition of a graph `G`. Modularity is a measure of the strength of division of a network into communities.\n\n- **Parameters**:\n - `G` (networkx.Graph): The input graph.\n - `partition` (list of sets or dict): The partition of the graph where each set (or dict) represents a community.\n \n- **Returns**:\n - `float`: The modularity score.\n\n### 2. `get_modularity(G, partition)`\nThis function calculates the modularity of the current partition using an alternative method based on node degrees and community assignments.\n\n- **Parameters**:\n - `G` (networkx.Graph): The graph for which modularity is to be calculated.\n - `partition` (dict): A dictionary where keys are nodes and values are community labels.\n \n- **Returns**:\n - `float`: The modularity score.\n\n### 3. `local_optimization_step(H, Q_max)`\nThis function performs a local optimization step on the graph to maximize modularity by moving nodes to neighboring communities.\n\n- **Parameters**:\n - `H` (networkx.Graph): The graph with community assignments as node attributes.\n - `Q_max` (float): The current maximum modularity.\n \n- **Returns**:\n - `float`: The updated maximum modularity after the optimization step.\n\n### 4. `network_aggregation_step(H)`\nThis function performs the network aggregation step by collapsing communities into super-nodes and recalculating edge weights between communities.\n\n- **Parameters**:\n - `H` (networkx.Graph): The graph where each node has a 'community' attribute.\n \n- **Returns**:\n - `networkx.Graph`: A new graph where nodes represent communities from the previous step.\n\n### 5. `reindex_communities(partition)`\nThis function reindexes the communities in the partition so that community labels are continuous.\n\n- **Parameters**:\n - `partition` (dict): A dictionary where keys are nodes and values are community labels.\n \n- **Returns**:\n - `dict`: A new partition where community labels are reindexed.\n\n### 6. `louvain_method(G, init=None)`\nThis function runs the Louvain method for community detection on a graph.\n\n- **Parameters**:\n - `G` (networkx.Graph): The input graph where nodes and edges define the structure.\n - `init` (dict): Optional initial partition.\n \n- **Returns**:\n - `dict`: The final partition of the graph with node assignments to communities.\n\n### 7. `vis_network_spring(G, best_partition, layout_type=\"spring_layout\")`\nThis function visualizes a network with a specified layout, coloring nodes by community.\n\n- **Parameters**:\n - `G` (networkx.Graph): The graph to visualize.\n - `best_partition` (dict): A partition of the graph nodes (community assignments).\n - `layout_type` (str): The layout algorithm to use. Options are \"spring_layout\", \"shell_layout\", and \"kamada_kawai_layout\".\n \n- **Returns**:\n - `None`: Displays the network graph.\n\n### 8. `vis_network_agg_spring(G, best_partition, layout1=\"shell_layout\", iterations=1)`\nThis function visualizes a network using an aggregated layout approach. The first layout is either 'shell_layout' or 'kamada_kawai_layout', and the second layout is always 'spring_layout' for a specified number of iterations.\n\n- **Parameters**:\n - `G` (networkx.Graph): The graph to visualize.\n - `best_partition` (dict): A partition of the graph nodes (community assignments).\n - `layout1` (str): The first layout algorithm to use, either 'shell_layout' or 'kamada_kawai_layout'.\n - `iterations` (int): The number of iterations for the 'spring_layout' adjustment.\n \n- **Returns**:\n - `None`: Displays the network graph.\n\n### 9. `vis_network_partition_process(G, pos=None, method=\"girvan_newman\", w=5.0, h=4.0, nrows=6, ncols=6, iterations_limit=None)`\nThis function visualizes the partitioning process of a network using the Girvan-Newman algorithm.\n\n- **Parameters**:\n - `G` (networkx.Graph): The input graph.\n - `pos` (dict or None): Positions for the nodes in the graph. If None, default spring_layout will be used.\n - `method` (str): Only \"girvan_newman\" is supported.\n - `w` (float): Width of each subplot.\n - `h` (float): Height of each subplot.\n - `nrows` (int): Number of rows in the grid of subplots.\n - `ncols` (int): Number of columns in the grid of subplots.\n - `iterations_limit` (int): Limit the number of iterations to display.\n \n- **Returns**:\n - `None`: Displays the partitioning process.\n",
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