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
The easy way (see https://pypi.org/project/multinetx/). Simply, open your terminal and write:
pip install multinetx
Otherwise, you simply download/clone the source files into the directory you keep your python scripts. Then you add that directory to your PYTHONPATH. In Unix/Linux you can do this by adding into your .bashrc file the two following lines:
export PYTHONPATH=/home/your_username/your_python_libs:$PYTHONPATH
export PYTHONPATH=/home/your_username/your_python_libs/multinetx:$PYTHONPATH
After request of some users I give here an example of how to "install" multinetx:
Create a directory for your python libraries (if you do not have already)
mkdir your_python_libs
Enter this directory
cd your_python_libs
Clone the multinetx
git clone https://github.com/nkoub/multinetx.git
Add multinetx to your PYTHONPATH by adding to your .bashrc the two following lines:
export PYTHONPATH=/home/your_username/your_python_libs:$PYTHONPATH
export PYTHONPATH=/home/your_username/your_python_libs/multinetx:$PYTHONPATH
import numpy as npimport multinetx as mxN = 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)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.Tmg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3],
inter_adjacency_matrix=adj_block)mg.set_edges_weights(intra_layer_edges_weight=2,
inter_layer_edges_weight=3)mg = mx.MultilayerGraph()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))mg.layers_interconnect(inter_adjacency_matrix=adj_block)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.
import numpy as np
import matplotlib.pyplot as pltimport multinetx as mxN = 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)mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3])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)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()
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.Tmg = 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)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()
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] = 1mg = 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)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()
If multiNetX was useful and facilitated your research and work flow you can use a reference in your publications by citing either of the following papers for which multiNetX was originally developed:
- R. Amato, N. E Kouvaris, M. San Miguel and A. Diaz-Guilera, Opinion competition dynamics on multiplex networks, New J. Phys. DOI: https://doi.org/10.1088/1367-2630/aa936a
- N. E. Kouvaris, S. Hata and A. Diaz-Guilera, Pattern formation in multiplex networks, Scientific Reports 5, 10840 (2015). http://www.nature.com/srep/2015/150604/srep10840/full/srep10840.html
- A. Sole-Ribata, M. De Domenico, N. E. Kouvaris, A. Diaz-Guilera, S. Gomez and A. Arenas, Spectral properties of the Laplacian of a multiplex network, Phys. Rev. E 88, 032807 (2013). http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.032807
(C) Copyright 2013-2017, Nikos E Kouvaris
Each file in this folder is part of the multiNetX package.
multiNetX is part of the deliverables of the LASAGNE project (multi-LAyer SpAtiotemporal Generalized NEtworks), EU/FP7-2012-STREP-318132 (http://complex.ffn.ub.es/~lasagne/)
multiNetX is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
multiNetX is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.