ugd 0.0.5

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.