gcmpy package

Submodules

gcmpy.distributions module

gcmpy.distributions.exponential(a: float) → Callable

Implemnts an exponential distribution. :param a: distribution parameter :returns p: callable

gcmpy.distributions.log_normal()

gcmpy.distributions.poisson(kmean: float) → Callable

Implements a poisson distribution.

Parameters

kmean – mean of poisson distribution

Returns p

Callable

gcmpy.distributions.power_law(alpha: float) → Callable

Implements a power law distribution with exponent alpha. Undefined for k = 0.

Parameters

alpha – power law exponent

Returns p

callable

gcmpy.distributions.scale_free_cut_off(alpha: float, kappa: float) → Callable

Implements a scale free with exponential degree cutoff function. Limits to scale free for large degree cutoff. Undefined for k = 0.

Parameters

• k – int degree

• alpha – float power law exponent

• kappa – float degree cutoff

gcmpy.distributions.weibull()

gcmpy.gcm_algorithm module

class gcmpy.gcm_algorithm.GCM_algorithm(motif_sizes: List[int], build_functions: List[Callable[[gcmpy.types._NODES], gcmpy.types._EDGES]])

Bases: object

Generalised configuration model algorithm.

Parameters

• num_networks – the number of networks to create

• motif_sizes – list of ints that indicate the number of nodes in each motif

• build_functions – callbacks that accept list of nodes and return edges

random_clustered_graph(jds: gcmpy.types._JDS) → gcmpy.utils.edge_list

Generate a random graph from a given joint degree sequence of motifs. If motif constructors are not specified, ValueError is raised.

Parameters

jds – joint degree sequence

Returns

a list of edges in the graph as an edge_list object

class gcmpy.gcm_algorithm.ResampleJDS(num_networks: int, motif_sizes: List[int], build_functions: List[Callable[[gcmpy.types._NODES], gcmpy.types._EDGES]], network_name: Optional[str] = None)

Bases: gcmpy.gcm_algorithm.GCM_algorithm

Resamples a joint degree sequence to create multiple networks.

Parameters

• num_networks – the number of networks to create

• motif_sizes – list of ints that indicate the number of nodes in each motif

• network_name – string identifier/classifier for network

• build_functions – callbacks that accept list of nodes and return edges

random_clustered_graph_from_resampled_jds(jds: gcmpy.types._JDS) → gcmpy.utils.results

Routine to create multiple configuration model networks from a single joint degree sequence. This essentially rewires a given sequence of joint degrees using the configuration model.

Parameters

jds – joint degree sequence

Returns results

data of constructed networks

gcmpy.joint_degree module

class gcmpy.joint_degree.JDD_Interface(modulo)

Bases: object

Joint degree distribution interface. Subclasses will define how self._jdd is created, and all implementations should do so upon construction.

Parameters

modulo – list of integers for number of nodes in each motif

convert_jds_to_jdd(jds: gcmpy.types._JDS)

Convert a joint degree sequence to self._jdd.

Parameters

jds – joint degree sequence

normalise_jdd()

Normalises self._jdd probability distribution.

sample_JDS(N: int) → gcmpy.types._JDS

Method to ensure the sum of the motifs in each dimension mod modulo[i] (which is the number of vertices in each motif) is zero by adding motifs to the motif list. This ensures the JDS is graphic.

Parameters

N – number of samples

Returns jds

joint degree sequnce

class gcmpy.joint_degree.JDD_delta_model(fp: Callable, modulo: List[int], probs: List[float], target_k: int, kmin: int, kmax: int)

Bases: gcmpy.joint_degree.JDD_split_K_model

A distribution of single edges apart from a specified target degree. For instance a distribution of degrees in a single dimension (2-cliques) with zeros for all other motif type counts, apart from when k=target.

create_jdd() → None

Creates self._jdd using the degree delta model.

class gcmpy.joint_degree.JDD_empirical_data(jds: gcmpy.types._JDS, modulo: List[int])

Bases: gcmpy.joint_degree.JDD_Interface

An empirical joint degree sequence is used to create self._jdd. :param jds: joint degree sequence

class gcmpy.joint_degree.JDD_joint_function(fp: Callable, modulo: List[int], hi_lo_degree_bounds: Tuple[int, int], use_sampling: bool = False, n_samples: int = 100000.0)

Bases: gcmpy.joint_degree.JDD_Interface

Multivariate function to evaluate the probability of given joint degree from an analytical source. Note, callable self._fp must accept a joint degree tuple and return a float.

Parameters

• fp – callback

• modulo – list of ints for number of vertices in each motif

• hi_lo_degree_bounds – list of tuples (int,int) for kmin,kmax per topology

• use_sampling – bool to use sampling or direct approach

• n_samples – number of samples if not direct

class gcmpy.joint_degree.JDD_manual(jdd: gcmpy.types._JDD, modulo: List[int])

Bases: gcmpy.joint_degree.JDD_Interface

Specify self._jdd by hand. :param jdd: joint degree distribution

class gcmpy.joint_degree.JDD_marginals(arr_fp: List[Callable], modulo: List[int], hi_lo_degree_bounds: List[Tuple[int, int]], use_sampling: bool = False, n_samples: int = 100000.0)

Bases: gcmpy.joint_degree.JDD_Interface

Merge uncorrelated marginals in each topology from analytical data together to create self._jdd. If using a direct method, all possible joint degree tuples are evaluated; however, for large varience in the allowed degrees this method is slow. Instead, we can choose to sample the analytical functions by setting use_sampling which draws n_samples weighted samples from each marginal function.

Parameters

• arr_fp – array of callbacks

• modulo – list of ints for number of vertices in each motif

• hi_lo_degree_bounds – list of tuples (int,int) for kmin,kmax per topology

• use_sampling – bool to use sampling or direct approach

• n_samples – number of samples if not direct

class gcmpy.joint_degree.JDD_split_K_model(fp: Callable, modulo: List[int], probs: List[float], kmin: int, kmax: int)

Bases: gcmpy.joint_degree.JDD_Interface

An overall degree distribution is split with probabilities of creating each motif.

calc_prob_of_joint_degree(jd: gcmpy.types._JOINT_DEGREE) → float

calculates the probability of a joint degree from the input params.

Parameters

jd – joint degree

Returns probability

float value

create_jdd() → None

Creates self._jdd using the split degree model

get_valid_joint_degrees(remaining_degree: int, topology: int) → List[gcmpy.types._JOINT_DEGREE]

Returns a list of tuples by recursion. Only an ordered list of cliques are currently supported.

Parameters

• remaining_degree – current free edges that can be partitioned

• topology – column index of joint degree tuple

:returns list of joint degrees

resolve_degree(k: int, prob_overall_k: float) → None

creates all valid joint degrees for overall k and their probability and updates self._jdd.

Parameters

• k – overall degree

• prob_overall_k – float value

gcmpy.motif_generators module

gcmpy.motif_generators.clique_motif(nodes: gcmpy.types._NODES) → List[gcmpy.types._EDGE]

Accepts list of ints and creates all possible pairs which it returns as a list of tuples of int pairs

Parameters

nodes – list of nodes (int)

Returns

edge list as list of tuples (int, int)

gcmpy.motif_generators.cycle_motif(nodes: gcmpy.types._NODES) → List[gcmpy.types._EDGE]

Accepts a list of ints and creates a cycle of adjacent node pairs. Creates two iterators and then increments one before zipping together to create tuples. Finally, connects the start and end of the chain toegher.

Parameters

nodes – list of nodes (int)

Returns

edge list as list of tuples (int, int)

gcmpy.motif_generators.diamond_motif(nodes: gcmpy.types._NODES) → List[gcmpy.types._EDGE]

Accepts list of ints and creates edge pairs for a diamond motif of 4 vertices.

Parameters

nodes – list of nodes (int)

Returns

edge list as list of tuples (int, int)

gcmpy.types module

gcmpy.utils module

class gcmpy.utils.edge_list

Bases: object

Network represented as an edge list. The GCM class uses this structure to generate networks which can then be converted to other network libraries.

add_edges_from(edges: gcmpy.types._EDGES) → None

Adds edges from list of tuples (int,int) to the edge list. :param edges: list of tuples of ints.

class gcmpy.utils.output_data(i: int)

Bases: object

An object to store output data from the process. :param i: integer for experiment index

class gcmpy.utils.results

Bases: object

A collection of output_data objects that can be serialised and converted to other graph formats.

add_result(r: gcmpy.utils.output_data) → None

read_results_from_binary_file(filename: str) → None

read the results structure from a binary file. :param filename: name of the file to read.

serialise_results_to_file(filename: str) → None

Dump the results structure to a binary file. :param filename: name of file to create.

to_iGraph() → List[any]

to_networkx() → List[any]

Module contents