README.md~

![png](logo.png) multiNetX v1.0 
=========

multiNetX is a python package for the manipulation and 
study 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
=========

multinetx does not need intallation. 
You simply download the source files and save them into your file system. 
Then you have to add that directory to your PYTHONPATH. 
In Unix/Linux you can do this by writting in the terminal the following command:
	
	export PYTHONPATH=path_to_your_python_libraries/multinetx:$PYTHONPATH



How to use multiNetX
=========


#### Import standard libraries for numerics


    import numpy as np

#### Import the package MultiNetX


    import multinetx as mx

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


    N = 8
    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)


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
    from scipy.sparse import lil_matrix

    import matplotlib.pyplot as plt

##### Import the package NetworkX and MultiNetX


    import networkx as nx
    import multinetx as mx

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


    N = 50
    g1 = nx.erdos_renyi_graph(N,0.07,seed=218)
    g2 = nx.erdos_renyi_graph(N,0.07,seed=211)
    g3 = nx.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])


##### Create the multiplex network with a different way


    MG = mx.MultilayerGraph()	# empty graph    
    MG.add_layer(g1)
    MG.add_layer(g2)
    MG.add_layer(g3) 
    MG.layers_interconnect() 	# zero inter-adjacency matrix


##### 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(nx.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,nx.fruchterman_reingold_layout(g1),
                          layer_vertical_shift=0.2,
                          layer_horizontal_shift=0.0,
                          proj_angle=47)
    nx.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](img/edge_colored.png)


#### Regular interconnected multiplex

##### Define the type of interconnection between the layers


    adj_block = 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(nx.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,nx.fruchterman_reingold_layout(MG.get_layer(0)),
                          layer_vertical_shift=1.4,
                          layer_horizontal_shift=0.0,
                          proj_angle=7)
    nx.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](img/regular_multiplex.png)


#### General multiplex multiplex 

##### Define the type of interconnection between the layers


    adj_block = 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=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)
    MG.set_intra_edges_weights(layer=3,weight=5)

##### Plot the adjacency matrix and the multiplex networks


    fig = plt.figure(figsize=(15,5))
    ax1 = fig.add_subplot(121)
    ax1.imshow(nx.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,nx.fruchterman_reingold_layout(MG.get_layer(0)),
                          layer_vertical_shift=.6,
                          layer_horizontal_shift=0.9,
                          proj_angle=.6)
    nx.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](img/general_multiplex.png)




Copyright
=========

(C) Copyright 2013-2015, 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/>.