netdecom 0.0.5.0

Dimensionality Reduction and Decomposition of Undirected Graph Models and Bayesian Networks

NetDecom Documentation

Overview

NetDecom is a Python package for advanced graph analysis, providing algorithms for convex subgraph extraction and recursive decomposition of both undirected graphs (UGs) and directed acyclic graphs (DAGs). Built on NetworkX, it offers efficient implementations of three core functionalities.

Installation

>>> pip install NetDecom

Core Functionalities

1. Convex Hull Identification in Undirected Graphs

Finds the minimal convex subgraph containing a given node set R:

>>> import NetDecom as nd
>>> import networkx as nx
>>> G = nx.Graph([(1, 2), (2, 3), (3, 4)])
>>> nd.IPA(G, [1, 3])  # Inducing Path Absorbing Algorithm
>>> nd.CMSA(G, [1, 3])  # Close Minimal Separator Absorbing Algorithm

2. Recursive Graph Decomposition

Decomposes graphs into maximal prime subgraphs using MCS ordering:

>>> MCS = [1, 2, 3, 4]  # Maximum Clique Sequence
>>> nd.Decom_CMSA((G, MCS))  # CMSA-based decomposition
>>> nd.Decom_IPA((G, MCS))  # IPA-based decomposition

3. Directed Convex Hull Identification in Directed Acyclic Graphs

Finds the minimal d-convex subgraph containing a given node set R:

>>> G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
>>> nd.CMDSA(G, {1, 3})  # Close Minimal D-Separator Absorbing Algorithm

4. Random Graph Generation

Generates random connected graphs, including UGs and DAGs, with specified parameters for node count and edge probability.

generator_connected_ug(n, p)

generate_connected_dag(n, p, max_parents=3)

Parameters:

• n (int): The number of nodes in the graph.
• p (float): The probability of adding an edge between any pair of nodes (for UG) or from a parent node to a child node (for DAG). The value should be between 0 and 1.
• max_parents (int, optional): The maximum number of parent nodes for each node in the DAG. Defaults to 3.

Returns:

• A connected graph (networkx.Graph for UG or networkx.DiGraph for DAG).

Example:

>>> ug = nd.generator_connected_ug(10, 0.3)  # Generate a connected UG with 10 nodes and edge probability 0.3
>>> dag = nd.generate_connected_dag(10, 0.3, max_parents=3)  # Generate a connected DAG with 10 nodes, edge probability 0.3, and maximum parents 3

5. Load Example Graphs

get_example(file_name)

Reads the specified example file from the library and returns the corresponding undirected NetworkX graph object.

Parameters:

• file_name (str): The name of the example file to be read. The following example files are available:

File Name	Nodes	Edges	Connected Components	Largest Component Size
mammalia-voles-rob-trapping-22.txt	103	151	15	59
Animal-Network.txt	445	1332	22	117
bio-CE-GT.txt	924	3239	13	878
bio-CE-GN.txt	2220	53683	3	2215
bio-DR-CX.txt	3289	84940	2	3287
DD6.txt	4152	10320	1	4152
as20000102.txt	6474	12572	1	6474
rec-movielens-user-movies-10m.txt	7601	55384	1	7601
CA-HepTh.txt	9875	25973	427	8638
rec-movielens-tag-movies-10m.txt	16528	71067	1	16528
CA-CondMat.txt	23133	93439	567	21363
Email-Enron.txt	36692	183831	1065	33696
rec-yelp-user-business.txt	50394	229572	19	50319
rec-eachmovie.txt	61989	2811458	1	61989
rec-movielens.txt	70155	9991339	1	70155
rec-amazon.txt	91813	125704	1	91813

Returns:

• A NetworkX UG object corresponding to the specified example file.

Example:

>>> G = nd.get_example("Email-Enron.txt")  # Load the Enron email network as an UG

Notes

• All input graphs must be NetworkX Graph/DiGraph objects.
• MCS ordering should follow graph topology.
• DAG decomposition features are under development.