pythagora.smallworld

module documentation

This module contains methods to initialize and compute metrics for a small-world simulation.

Function	`clustering_coefficient`	Returns the average clustering coefficient for specified graph. This is a shortcut method to the `average_clustering()` method from NetworkX.
Function	`connect_initial_communities`	Connects communities at the start of the simulation.
Function	`form_community_lattice`	Instantiate a Graph and construct a lattice containing all community members.
Function	`form_community_lattices`	Instantiate a graph and add a group of communities in lattice structures.
Function	`form_dense_communities`	Returns a graph of fully connected communities.
Function	`form_dense_community`	Returns a graph with all possible edges added.
Function	`get_SWI_index`	Computes small world index (SWI).
Function	`initialize_small_world`	Sets up a small world graph for an experiment.
Function	`is_small_world`	Checks if a network qualifies as a small world.
Function	`make_lattice_from_nodes`	Construct a lattice structure out of existing nodes.
Function	`make_small_world_graph_info_file`	Creates an information file (.csv) for this small world experiment.
Function	`net_avg_degree`	Returns average degree of nodes in a graph.
Function	`small_world_rewire`	Rewires the small world network.

def clustering_coefficient(G): ¶

Returns the average clustering coefficient for specified graph. This is a shortcut method to the `average_clustering()` method from NetworkX.

A clustering coefficient is a measure of how much nodes cluster together in a graph.

Parameters
G	target graph for computation
Returns
average clustering coefficient for specified graph

def connect_initial_communities(G): ¶

Connects communities at the start of the simulation.

Parameters
G	graph containing disconnected communities
Returns
graph containing connected communities

def form_community_lattice(community): ¶

Instantiate a Graph and construct a lattice containing all community members.

Parameters
community	community containing buyers/members
Returns
NetworkX Graph object in lattice structure

def form_community_lattices(community_set): ¶

Instantiate a graph and add a group of communities in lattice structures.

Parameters
community_set	list of communities (with members) to add (CommunitySet)
Returns
NetworkX Graph object with communities in lattice structure

def form_dense_communities(community_set): ¶

Returns a graph of fully connected communities.

Parameters
community_set	List of communities (CommunitySet)
Returns
a graph of fully connected communities

def form_dense_community(community): ¶

Returns a graph with all possible edges added.

Parameters
community	community of buyers to fully connect
Returns
a fully connected community of buyers

def get_SWI_index(G): ¶

Computes small world index (SWI).

Let n be the number of nodes in the graph. Let k be the average degree of nodes in the graph. Let L_path be the average shortest path length of nodes in the graph.

Parameters
G	target graph for computation
Returns
small world index of inputted graph

def initialize_small_world(num_buyers, num_communities, min_community_fill, assemblage, community_structure='dense'): ¶

Sets up a small world graph for an experiment.

Parameters
num_buyers	number of buyers in market
num_communities	number of communities in market
min_community_fill	minimum number of buyers per community
assemblage	list of items for sale in market
community_structure	structure to initialize communities; can be dense or lattice (default: dense)
Returns
small world graph of communities

def is_small_world(G, small_world_index_threshold=0.5): ¶

Checks if a network qualifies as a small world.

Parameters
G	potential small world network
small_world_index_threshold	qualifying SWI
Returns
True if qualifies as small world, False otherwise

def make_lattice_from_nodes(G): ¶

Construct a lattice structure out of existing nodes.

Parameters
G	NetworkX graph object containing nodes
Returns
restructured NetworkX graph object

def make_small_world_graph_info_file(num_buyers, min_num_communities, min_community_fill, assemblage, epochs, upper_thresh, lower_thresh, death_thresh, results_dir, prob_rewire, start_structure): ¶

Creates an information file (.csv) for this small world experiment.

Parameters
num_buyers	number of buyers in market
min_num_communities	minimum number of communities
min_community_fill	minimum number of buyers per community
assemblage	list of items for sale in market
epochs	number of market iterations
upper_thresh	% of buyers that must own a particular item to change a buyer's intention to that item
lower_thresh	max % of buyers that may own a particular item to change a buyer's intention to random item
death_thresh	percentage at which a pot is removed from the market
results_dir	directory path in which to store the file
prob_rewire	probability that a node is rewired each epoch
start_structure	structure in which communities are initialized (dense or lattice)

def net_avg_degree(G): ¶

Returns average degree of nodes in a graph.

Parameters
G	target graph for computation
Returns
average degree of nodes in a graph

def small_world_rewire(G, prob_rewire, epoch, logger): ¶

Rewires the small world network.

Parameters
G	current network structure
prob_rewire	probability of rewire for each node
epoch	current epoch (for logger)
logger	logging object
Returns
rewired graph