multiNetX v2.3

multiNetX is a python package for the manipulation and visualization of multilayer networks. The core of this package is a MultilayerGraph, a class that inherits all properties from networkx.Graph().

This allows for:

Creating networks with weighted or unweighted links (only undirected networks are supported in this version)
Analysing the spectral properties of adjacency or Laplacian matrices
Visualizing dynamical processes by coloring the nodes and links accordingly

How to install multiNetX

You have to execute the following command in your terminal:

pip install git+https://github.com/nkoub/multinetx.git

Clone the repository of multinetx into your system:
```
git clone https://github.com/nkoub/multinetx.git
```
Enter in the multinetx directory:
```
cd multinetx
```
and then simply write:
```
pip install .
```

How to use multiNetX

Import standard libraries for numerics

import numpy as np

Import the package MultiNetX

import multinetx as mx

Create a multiplex 1st way

Create three Erd"os- R'enyi networks with N nodes for each layer

N = 5
g1 = mx.generators.erdos_renyi_graph(N,0.5,seed=218)
g2 = mx.generators.erdos_renyi_graph(N,0.6,seed=211)
g3 = mx.generators.erdos_renyi_graph(N,0.7,seed=208)

Create an 3Nx3N lil sparse matrix. It will be used to describe the layers interconnection

adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))

Define the type of interconnection among the layers (here we use identity matrices thus connecting one-to-one the nodes among layers)

adj_block[0:  N,  N:2*N] = np.identity(N)    # L_12
adj_block[0:  N,2*N:3*N] = np.identity(N)    # L_13
adj_block[N:2*N,2*N:3*N] = np.identity(N)    # L_23
    
# use symmetric inter-adjacency matrix
adj_block += adj_block.T

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3],
                        inter_adjacency_matrix=adj_block)

Weights can be added to the edges

mg.set_edges_weights(intra_layer_edges_weight=2,
                     inter_layer_edges_weight=3)

Create a multiplex 2nd way

mg = mx.MultilayerGraph()

Add layers

mg.add_layer(mx.generators.erdos_renyi_graph(N,0.5,seed=218))
mg.add_layer(mx.generators.erdos_renyi_graph(N,0.6,seed=211))
mg.add_layer(mx.generators.erdos_renyi_graph(N,0.7,seed=208))

Create an instance of the MultilayerGraph class

mg.layers_interconnect(inter_adjacency_matrix=adj_block)

Weights can be added to the edges

mg.set_edges_weights(intra_layer_edges_weight=2,
                     inter_layer_edges_weight=3)

The object mg inherits all properties from Graph of networkX, so that we can calculate adjacency or Laplacian matrices, their eigenvalues, etc.

How to plot multiplex networks

Import standard libraries

import numpy as np
import matplotlib.pyplot as plt

Import the package MultiNetX

import multinetx as mx

Create three Erd"os- R'enyi networks with N nodes for each layer

N = 50
g1 = mx.erdos_renyi_graph(N,0.07,seed=218)
g2 = mx.erdos_renyi_graph(N,0.07,seed=211)
g3 = mx.erdos_renyi_graph(N,0.07,seed=208)

Edge colored nertwork (no inter-connected layers)

Create the multiplex network

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3])

Set weights to the edges

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('edge colored network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(g1),
					  layer_vertical_shift=0.2,
					  layer_horizontal_shift=0.0,
					  proj_angle=47)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

png

Regular interconnected multiplex

Define the type of interconnection between the layers

adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))

adj_block[0:  N,  N:2*N] = np.identity(N)    # L_12
adj_block[0:  N,2*N:3*N] = np.identity(N)    # L_13
#adj_block[N:2*N,2*N:3*N] = np.identity(N)    # L_23
adj_block += adj_block.T

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3], 
						inter_adjacency_matrix=adj_block)

mg.set_edges_weights(inter_layer_edges_weight=4)

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('regular interconnected network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(mg.get_layer(0)),
					  layer_vertical_shift=1.4,
					  layer_horizontal_shift=0.0,
					  proj_angle=7)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

png

General multiplex multiplex

Define the type of interconnection between the layers

adj_block = mx.lil_matrix(np.zeros((N*4,N*4)))

adj_block[0  :  N ,   N:2*N] = np.identity(N)   # L_12
adj_block[0  :  N , 2*N:3*N] = np.random.poisson(0.005,size=(N,N))   # L_13
adj_block[0  :  N , 3*N:4*N] = np.random.poisson(0.006,size=(N,N))   # L_34
adj_block[3*N:4*N , 2*N:3*N] = np.random.poisson(0.008,size=(N,N))   # L_14
adj_block += adj_block.T
adj_block[adj_block>1] = 1

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3,g1],
						inter_adjacency_matrix=adj_block)

mg.set_edges_weights(inter_layer_edges_weight=5)

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)
mg.set_intra_edges_weights(layer=3,weight=4)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('general multiplex network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(mg.get_layer(0)),
					  layer_vertical_shift=.3,
					  layer_horizontal_shift=0.9,
					  proj_angle=.2)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

png

How to plot 3D multiplex networks

Import specific libraries

import numpy as np #  to use matrix
import matplotlib.pyplot as plt # to use plot
import networkx as nx # to use graphs
import multinetx as mx # to use multinet
import math # to use floor
import matplotlib.cm as cmx # to use cmap (for data color values)
import matplotlib.colors as colors # to use cmap (for data color values)
import matplotlib.cbook as cb # to test if an object is a string

from mpl_toolkits.mplot3d import Axes3D # to use 3D plot

Create multinet

N1 = 10
g1 = nx.cycle_graph(N1)
N2 = 2*N1
g2 = nx.cycle_graph(N2)

adj_block = mx.lil_matrix(np.zeros((N1+N2,N1+N2)))

for i in range(N1):
    adj_block[i,N1+2*i] = 1

adj_block += adj_block.T

mg = mx.MultilayerGraph(list_of_layers=[g1,g2],inter_adjacency_matrix=adj_block)

Plot multiplex networks by layer

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')

pos = mx.get_position3D(mg)


intra_c = ['b','r']
inter_c = 'grey'
layer_c = ['b','r']

mg.set_edges_weights(inter_layer_edges_weight=1, intra_layer_edges_weight=1)
edge_color=[mg[a][b]['weight'] for a,b in mg.edges()]


mx.FigureByLayer(mg, pos, ax, intra_edge_color=intra_c,node_color=layer_c, inter_edge_color=inter_c)
ax.axis('off')

png

(-1.0999999812245371,
 1.0999999991059304,
 -1.0999999595281706,
 1.0999999980727702)

Plot multiplex networks by nodes and edges

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')
# Get position of all nodes
pos = mx.get_position3D(mg)
# Set edges weights
mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_edges_weights(inter_layer_edges_weight=3)

# Get edges and nodes color
edge_color=[mg.edges.get((a,b))['weight'] for a,b in mg.edges()]
node_color=[i for i in mg.nodes]

# Plot multiplex network using options
mx.Figure3D(mg, pos, ax, edge_color=edge_color, node_color=node_color, 
         node_shape = 'D', edge_linewidth = 0.5, node_linewidth = 0,
         edge_style = 'dashed', label = 'Node', wit

Multinetx

Install / Use

README

multiNetX v2.3

How to install multiNetX

How to use multiNetX

Import standard libraries for numerics

Import the package MultiNetX

Create a multiplex 1st way

Create three Erd"os- R'enyi networks with N nodes for each layer

Create an 3Nx3N lil sparse matrix. It will be used to describe the layers interconnection

Define the type of interconnection among the layers (here we use identity matrices thus connecting one-to-one the nodes among layers)

Create an instance of the MultilayerGraph class

Weights can be added to the edges

Create a multiplex 2nd way

Add layers

Create an instance of the MultilayerGraph class

Weights can be added to the edges

How to plot multiplex networks

Import standard libraries

Import the package MultiNetX

Create three Erd"os- R'enyi networks with N nodes for each layer

Edge colored nertwork (no inter-connected layers)

Create the multiplex network

Set weights to the edges

Plot the adjacency matrix and the multiplex networks

Regular interconnected multiplex

Define the type of interconnection between the layers

Create an instance of the MultilayerGraph class

Plot the adjacency matrix and the multiplex networks

General multiplex multiplex

Define the type of interconnection between the layers

Create an instance of the MultilayerGraph class

Plot the adjacency matrix and the multiplex networks

How to plot 3D multiplex networks

Import specific libraries

Create multinet

Plot multiplex networks by layer

Plot multiplex networks by nodes and edges

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