ugd 0.0.8

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

Uniform Graph Draw

currently in production

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

It is implement according to the papers:

• ...

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

Get it running

Install the paper via pip:

• pip install ugd

then run

#import modules
import ugd
import numpy

# create ajdancy matrix
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

# create dictionary of nodeatributes 
var_dict ={
    0: {'gender': 'm'},
    1: {'gender': 'm'},
    2: {'gender': 'f'},
    3: {'gender': 'f'},
}
graphs, stats_list = ugd.graph_hyp_test(adj_m=adj_m, var_dict = var_dict, test_variable= ('gender','m','f'),mixing_time=1000, anz_sim=100, show_polt=True)

API

There are two functions provided.

1. graph_hyp_test
   • generating a sequence of uniform sampled graphs under the desired set of constrains.
2. digraph_hyp_test
   • generating a sequence of uniform sampled digraphs under the desired set of constrains.

For the API fo the two functions only differs in that the interpretation of the adjancy matrix is once as digraph representation and once as graph representation.

INPUT:
:param adj_m:         A numpy array containing 0 and 1s as elements, representing
                      adjacency matrix of the graph
:param var_dict:      A dictionary with the integers 1..n as primary key (representing
                      the n nodes). The values are dictionaries containing the 
                      Variable name as keys and the values can either be numbers or be
                      numbers or strings
:param stat_f:        A function which maps the adj_m and var_dict to a number "the
                      statistic of interest".
:param test_variable: alternative to stat_f, creating a statistic which counts the
                      arrows form a node-subset into another. It is a triple with 
                      first element variable name, second the value of the variable 
                      for the set where the arrows leave and third the value of the 
                      subset where the arrow go to.
:param controlls:     List of variable names, the number of arrows crossing the groups
                      induced by the controls is constant in all the simulation.
:param mixing_time:   Number of runs (steps in the markov graph) before a the graph
                      is considered random
:param anz_sim:       Number of simulations
:param show_polt:     Boolean whether a plot is desired

OUTPUT:
:return:
graph_list:           List of random adjacency matrices with the given degree-sequence
                      and arrows between the controls
stats_list:           List of the statistics stat_f evaluated for the random graphs

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

• markow_walk

  Implementation of algorithm 1 from the paper ....

• schlaufen_construction

  Implementation of algorithm 2 from the paper ....

• model

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

• user_interface

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

• help_functions

Testing

All tests are in the test folder. They are written using pytest. To execute them cd into the test folder and run

• pytest

in the terminal.