pymnet.MultilayerNetwork¶

class pymnet.MultilayerNetwork(aspects=0, noEdge=0, directed=False, fullyInterconnected=True)¶

General multilayer network with a tensor-like interface.

See Reference [1] for background on the definition of this class.

There are several ways of accessing the edges and nodes of the network. If there is a single aspect, then the following notation can be used:

>>> net[i,s]                   #node i at layer s
>>> net[i,j,s,r]               #edge between nodes i and j and layers s and r
>>> net[i,j,s] == net[i,j,s,s] #edge between nodes i and j at layer s

Following slicing notation can also be used:

>>> net[i,:,s,:] == net[i,s]   #node i at layer s
>>> net[i,j,s,:]               #node i at layer s, but only links to j are visible
>>> net[i,:,s,r]               #node i at layer s, but only links to layer r are visible
>>> net[i,:,s] == net[i,:,s,s]

Similar notation holds for two (or more) aspects:

>>> net[i,s,x]                 #node i at layer s in aspect 1 and at layer x in aspect 2
>>> net[i,j,s,x]               #link i,j at layer s in aspect 1 and layer x in aspect 2 = i,j,s,s,x,x
>>> net[i,j,s,r,x,y]           #link i,j between layers s and r in aspect 1 and between layers x and y in aspect 2
>>> net[i,:,s,:,x,:] == net[i,s,x]
>>> net[i,j,s,:,x,y]           #node i at layer s and y, but only links to j and y are visible
>>> net[i,:,s,x] == net[i,:,s,s,x,x]

Parameters:

aspectsint: Number of aspects
noEdgeobject: Any object signifying that there is no edge.
directedbool: True if the network is directed, otherwise it’s undirected.
fullyInterconnectedbool: Determines if the network is fully interconnected, i.e. all nodes are shared between all layers. Ignored if aspects==0.

See also

MultiplexNetwork: A class for multiplex networks

Notes

The default data structure behind this class is a graph similar to the one described in Reference [1] implemented with nested dictionaries. The downside to this implementation is that, for example, iterating through all the inter-layer links is not possible without inspecting also the inter-layer links.

References

[1] Multilayer Networks. Mikko Kivela, Alexandre Arenas, Marc Barthelemy, James P. Gleeson, Yamir Moreno, Mason A. Porter, arXiv:1309.7233 [physics.soc-ph]

Attributes:

edges

Methods

`add_layer`(layer[, aspect])	Adds an empty layer to the network.
`add_node`(node[, layer])	Adds an empty node to the network.
`get_layers`([aspect])	Return the set of (elementary) layers (in a given aspect).
`get_supra_adjacency_matrix`([includeCouplings])	Return the supra-adjacency matrix and a list of node-layer pairs.
`iter_layers`([aspect])	Iterate over all layers.
`iter_node_layers`()	Iterate over all node-layer pairs.
`iter_nodes`([layer])	Iterate over nodes in the network.

__init__(aspects=0, noEdge=0, directed=False, fullyInterconnected=True)¶

Methods

`__init__`([aspects, noEdge, directed, ...])
`add_layer`(layer[, aspect])	Adds an empty layer to the network.
`add_node`(node[, layer])	Adds an empty node to the network.
`get_layers`([aspect])	Return the set of (elementary) layers (in a given aspect).
`get_supra_adjacency_matrix`([includeCouplings])	Return the supra-adjacency matrix and a list of node-layer pairs.
`iter_layers`([aspect])	Iterate over all layers.
`iter_node_layers`()	Iterate over all node-layer pairs.
`iter_nodes`([layer])	Iterate over nodes in the network.

Attributes

edges