ugd 0.0.1

drawing uniformly graphs under constraint. Commonly used for the estimation of the test distribution

Markov Chain Draw

currently in porduction

This package implements random draw algorithm for networks. In particular it creates uniform samples of networks with a given degreesequence and further constraints (fixed number of crossing edges/arrows between node-groups)

It is implementd according to the paper:

• ...

The paper also include a proof of correctness and a discussion of the statistical background.

Get it running

Install the paper via pip:

• pip install mcd

then run

 import mcd
 import numpy
    adj_m = numpy.zeros((4,4))
    adj_m[0,1] = 1
    adj_m[1,0] = 1
    adj_m[3,2] = 1
    adj_m[2,3] = 1
    var_dict ={
        0: {'gender': 'm'},
        1: {'gender': 'm'},
        2: {'gender': 'f'},
        3: {'gender': 'f'},
    }
    graphs, stats_list = graph_hyp_test(adj_m=adj_m, var_dict = var_dict, test_variable= ('gender','m','f'),mixing_time=10000, anz_sim=100, show_polt=True)

For an illustration more extensive use cases, see the examples scripts in:

• www.github/mcd.com ....

API

There are two functions provided.

• digraph_hyp_test
  • generating a sequence of uniform sapled digraphs under the desired set of constrains.
• graph_hyp_test
  • generating a sequence of uniform sapled digraphs under the desired set of constrains.

For a exact API documentation as well as a usage examples see the function documentation.

Comment:

The current implementation, includes only controlling of a fixed number of crossing edges/arrows between node-groups as constraints. More complex complex can be implemented by writing a consum implementation of the no_violation function in constraint_violation_check. Note, that depending on the constraint the construction of the Schlaufensequence should not be stopped because a feasible one is found, but only due to the random stop. This in order to preserve correctness.

Architecture:

All the logic is implemented in the digraph_draw folder. it is divided into

• model

  • containing the data models (appropriate Graph representation and node representation for efficient construction of the altering paths in the Schlaufen)

• high_level_intervace

  Contains the all the logic used for input validation, parsing of input, estimation of runtime, transformation of the graph format, output processing.

• help_functions

The actual logic for sampling the graphs is in:

• markow_walk * Implementation of algoritm "" from the paper ....

• schlaufen_construction * Implementation of algoritm "" from the paper ....

Testing

based on pytest. cd into mcd directory and run

• pytest

Todo

• implement, or modies the existing tests for bouth cases