netd 0.1

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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.