multisoc

multisoc is a python package to simulate and analyze networks with multidimensional interactions.

The code also reproduces the results from the paper The hidden architecture of connections: How do multidimensional identities shape our social networks?.
Preprint available at https://arxiv.org/abs/2406.17043.

Installation

Install the latest version:

pip install multisoc

Install from source:

git clone https://github.com/CSHVienna/multisoc
cd multisoc
pip install -e .

Examples

Multidimensional graph generation

In this example, we generate a graph, with two attributes and two categories per attribute, using the multidimensional_network_fix_av_degree function.
The graph is very homophilic in the first attribute, and slightly homophilic in the second one. Furthermore, the population distributions of the two attributes are slightly correlated.

import numpy as np
from multisoc.generate.multidimensional_network import multidimensional_network_fix_av_degree
from multisoc.generate.two_dimensional_population import consol_comp_pop_frac_tnsr

## List of 1d homophily matrices (2 for a two-dimensional system)
h_mtrx_lst = [ 
    np.array([[0.9,0.1],
              [0.1,0.9]]),
    np.array([[0.6,0.4],
              [0.4,0.6]])
]

## The marginals of the population distribution defined by comp_pop_frac_tnsr
## Each row has to sum 1 (100% of the population)
pop_fracs_lst = [
    [0.2,0.8],
    [0.4,0.6]
]

## Generate population distribution with certain level of correlation between the two attributes
## No correlation would correspond to the fraction of the largest minority
consol = 0.4 ## Level of correlation
comp_pop_frac_tnsr = consol_comp_pop_frac_tnsr(pop_fracs_lst,consol)

N = 200 ## Number of nodes
m = 20  ## Average number of connections per node

kind = "all" ## Aggregation function: {all->and, one->mean, any->or}
p_d = [0.5, 0.5] ## Weight of each dimension for "mean" aggregation function

G = multidimensional_network_fix_av_degree(
                h_mtrx_lst,
                comp_pop_frac_tnsr,
                kind,
                directed=False, ## Directed or undirected network
                pop_fracs_lst = pop_fracs_lst,
                N=N,
                m=m,
                v = 0,
                p_d = p_d
                )

Inference of multidimensional interactions

In this example, we infer the one-dimensional preferences and the aggregation function, given a dummy dataset that contains three attributes: number, color and shape. After the code, you can see how the input data is structured.
In particular, we print the value of AIC for the model that uses the AND aggregation function.

from multisoc.infer import data_loader
from multisoc.infer import wrappers
import pandas as pd

# Load the data
nodes_dummy = pd.read_csv("./dummy_data/nodes_dummy.csv",index_col="index",dtype='category')
edges_dummy = pd.read_csv("./dummy_data/edges_dummy.csv",dtype='category')

# Describe the type of data 
dimensions_list = ['number','color','shape']
shape_list = ["Circle","Square"]
color_list = ["Blue","Red"]
number_list = ["1","2","3","4","5","6"]
all_attributes_dict = {
    "shape":shape_list,
    "color":color_list,
    "number":number_list
}

# Compute the result dictionary, if we suppose that the data was generated using the AND aggregation function
nodes_input, edges_input = data_loader.build_nodes_edges_input_df(nodes_dummy, edges_dummy, dimensions=["shape","color","number"])
results_1d_dct = wrappers.infer_latent_preferences_1dSimple(
    nodes_input,
    edges_input,
    dimensions_list, 
    all_attributes_dict,
    type_p = "and" ## Type of aggregation function {and,or,mean}
    )

# Print the AIC
print(results_1d_dct['AIC'])

The nodes_dummy.csv file contains the information related to the nodes' attributes.
Each row contains the index of the node, and the corresponding attributes.

index	shape	color	number
0	Square	Blue	3
1	Circle	Blue	3
2	Square	Red	5
3	Square	Blue	3
4	Square	Red	1

The edges_dummy.csv file contains the information related to the connection among the individuals.
Each row contains one edge, with the corresponding source and target nodes.

	source	target
0	0	1
1	0	23
2	0	41
3	0	63
4	0	103