graphy.graphgen - Module to generate structured graphs

Module implementing tools to generate graphs and connectivity matrices. Generally, gen_... functions return generatively-created objects, while get_... return graphs corresponding to passed in membership vectors.

Use sample_connection_matrix to generate binary connectivity matrices sampled from matrices of connection probabilities.

graphy.graphgen.gen_ring_matrix(N, neighs_per_side=1)

Generate a ring-lattice matrix.

For example:

>>> import graphy
>>> mx = graphy.graphgen.gen_ring_matrix(30, 5)
>>> graphy.plotting.plot_graph(mx) 

(Source code, png, hires.png, pdf)

Parameters:

Nint

How many nodes.

neighs_per_sideint

How many neighbors on each side should be connected to each node.

Returns:

np.array matrix

The connectivity matrix

graphy.graphgen.get_clique_of_rings_net_and_pos(sizes, neighs_per_side=1, ring_weight=1.0, clique_weight=1.0)

Generate several ring-lattice graphs of different sizes. Then choose a single node from each ring and interconnect those into a clique.

>>> import graphy
>>> net, pos = graphy.graphgen.get_clique_of_rings_net_and_pos([5, 10, 20])
>>> graphy.plotting.plot_graph(net, pos=pos) 

(Source code, png, hires.png, pdf)

Parameters:

sizeslist of int

How many nodes in each ring.

neighs_per_sideint or list (default 1)

For nodes in ring lattices, how many neighbors on each side to connect to. If list, specifying the neighbors on each side within the corresponding ring.

ring_weightfloat (default 1.0)

Strength of connections in each ring lattice.

clique_weightfloat (default 1.0)

Strength of connections in clique connecting single nodes in each ring.

Returns:

networkx graph

The clique of rings network

dict

{ node : xyposition } dictionary of positions for good node layout

graphy.graphgen.gen_hierarchical_net(n, level)

Generate hiearchical graph using method proposed of: Ravasz E, Barabasi AL, Hierarchical organization in complex networks, PRE, 2003.

Parameters:

nint

Number of nodes in the lowest level.

levelint

Number of hierarchical levels to create

Returns:

networkx graph

The hierchically-structured network

graphy.graphgen.get_hierarchical_net_pos(net)

Get x,y positions for plotting hierarchical graph.

For example:

>>> import graphy
>>> G = graphy.graphgen.gen_hierarchical_net(5, 2)
>>> pos = graphy.graphgen.get_hierarchical_net_pos(G)
>>> graphy.plotting.plot_graph(G, pos=pos)

(Source code, png, hires.png, pdf)

Parameters:

netnetworkx graph

Graph whose nodes to layout

Returns:

dict

Dictionary containing node:(x,y) entries

graphy.graphgen.sample_connection_matrix(prob_mx)

Sample from a matrix of connection probabilities in order to create a binary connection matrix with 0s on the diagonal.

Parameters:

prob_mx2-dimensional np.array of floats

Matrix of connection probabilities

Returns:

2-dimensional np.array

Binary connectivity matrix

graphy.graphgen.get_weighted_block_matrix(membership, intra_community_w, inter_community_w)

Get weighted block-structured matrix corresponding to membership vector with different weights for intra- versus inter-community connections, and 0s on the diagonals.

For example:

>>> from graphy import graphgen
>>> cmx = graphgen.get_weighted_block_matrix([0,0,0,0,0,1,1,1,1,1], 0.5, 0.1)
>>> plt.imshow(cmx, interpolation='none') 

(Source code, png, hires.png, pdf)

Parameters:

membershiplist or np.array of ints

Array containing assignment of each node to communities

intra_community_wfloat

Weight for intra-community connections

inter_community_wfloat

Weight for inter-community connections

Returns:

np.array matrix

The connectivity matrix

graphy.graphgen.gen_hierarchical_weighted_block_matrix(blocksize, numblocks, numlevels, level_weights)

Generate hierarchical weighted block matrix.

For example:

>>> from graphy import graphgen
>>> cmx = graphgen.gen_hierarchical_weighted_block_matrix(4, 4, 2, [0.3, 0.2, 0.1])
>>> plt.imshow(cmx, interpolation='none') 

(Source code, png, hires.png, pdf)

Parameters:

blocksizeint

Number of nodes to include in each lowest-level block

numblocksint

Number of blocks each level consists of

numlevelsint

Number of levels

level_weightslist of float

Strength of connection between members for each level (plus one more for the ‘top’ level). Order is from lowest-level (smallest blocks) to highest-level

Returns:

np.array matrix

The generated connectivity matrix

graphy.graphgen.get_barbell_matrix(membership, num_conns=1)

Get a matrix of completely-connected communities connected by paths corresponding to membership vector.

For example:

>>> from graphy import graphgen
>>> cmx = graphgen.get_barbell_matrix([0,0,0,0,0,1,1,1,1,1])
>>> import matplotlib.pylab as plt
>>> plt.imshow(cmx, interpolation='none') 

(Source code, png, hires.png, pdf)

Parameters:

membershiplist or np.array of ints

Array containing assignment of each node to communities

num_connsint

Number of links that should run between communities

Returns:

np.array matrix

The connectivity matrix