Efficient Sampling of Directed Graphs

This repo contains an efficient implementation of the idea proposed in Constructing and Sampling Directed Graphs with Linearly Rescaled Degree Matrices.

The algorithm constructed a small graph from the original graph using Joint Degree Matrix and Degree Correlation Matrix (see paper for more details).

Dependencies

python
networkx
numpy
scipy

Usage of Main Algorithm

The main algorithm is implemented in src/sample.py

sample(G, k, file_name)

Inputs: G: The original graph (nx.DiGraph); k: input_sample_ratio (float, within (0,1)); file_name: the name of the original graph (defined by user, a folder for storing output files will be created at results/[file_name])

Returns: time_list: time used in each step (python list); number of duplicate edges: int

Outputs: edgelist: stored as results/[file_name]/sampled_[k]_edge_list.txt (using nx.write_edgelist); degree_sequence: stored as results/[file_name]/sampled_[k]_degree_sequence.txt formatted as {ind},{outd}, each row correponds to one node in the sampled graph

An Easy Example

import networkx as nx
from src import sample

er = nx.fast_gnp_random_graph(1000, 1e-3,directed=True) # create an Erdős-Rényi graph
time_list, duplicate = sample.sample(er, 0.1, 'erdos_renyi_graph') # sample the graph
er_sampled = nx.read_edgelist("results/erdos_renyi_graph/sampled_0.1_edge_list.txt", create_using=nx.DiGraph(), data=False)  # reads back the sampled graph

Advanced Usage

This repo also contains the following content for advanced usage.

• data: folder where 10 synthetic datasets (5 Erdős-Rényi graphs, 5 scale-free graphs) and 8 real-world datasets (from The KONECT Project) are stored.
• results: folder where sampling results are stored. For the 10 datasets in data folder, the sampled graph (k=0.75) and a range of related files are given
• src: folder where the main algorithm (sample.py) and many helper files are stored.
• experiment.sh: shellcode to automatically run all kinds of experiments with arguments (-re: --run-experiments, -gd: --run-experiments, -god: --run-experiments, -pd: --run-experiments, -gfd: --run-experiments, -fpl: --run-experiments). sample_ratio needs to be specified at the top of the shellcode