cpnet package

Submodules

cpnet.BE module

class cpnet.BE.BE(num_runs=10)

Bases: CPAlgorithm

Borgatti Everett algorithm.

Algorithm for finding single core-periphery pair in networks.

19. 16. Borgatti and M. G. Everett. Models of core/periphery structures. Social Networks, 21, 375–395, 2000

>>> import cpnet
>>> be = cpnet.BE()
>>> be.detect(G)
>>> pair_id = be.get_pair_id()
>>> coreness = be.get_coreness()

Note

• [ ] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

cpnet.CPAlgorithm module

class cpnet.CPAlgorithm.CPAlgorithm

Bases: object

depairing(labels, d)

abstract detect()

Private.

get_coreness()

Get the coreness of each node.

get_pair_id()

pairing(labels, a)

score(G, c, x)

Get score of core-periphery pairs.

cpnet.Cucuringu module

class cpnet.Cucuringu.LapCore(beta=0.1)

Bases: CPAlgorithm

LapCore algorithm.

13. Cucuringu, P. Rombach, S. H. Lee, and M. A. Porter Detection of core-periphery structure in networks using spectral methods and geodesic paths. Euro. J. Appl. Math., 27:846–887, 2016.

>>> import cpnet
>>> lc = cpnet.LapCore()
>>> lc.detect(G)
>>> pair_id = lc.get_pair_id()
>>> coreness = lc.get_coreness()

Note

• [ ] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

class cpnet.Cucuringu.LapSgnCore(beta=0.1)

Bases: CPAlgorithm

LowSgnCore algorithm.

13. Cucuringu, P. Rombach, S. H. Lee, and M. A. Porter Detection of core-periphery structure in networks using spectral methods and geodesic paths. Euro. J. Appl. Math., 27:846–887, 2016.

>>> import cpnet
>>> lsc = cpnet.LapSgnCore()
>>> lsc.detect(G)
>>> pair_id = lsc.get_pair_id()
>>> coreness = lsc.get_coreness()

Note

• [ ] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect a single core-periphery pair.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

class cpnet.Cucuringu.LowRankCore(beta=0.1)

Bases: CPAlgorithm

LowRankCore algorithm.

13. Cucuringu, P. Rombach, S. H. Lee, and M. A. Porter Detection of core-periphery structure in networks using spectral methods and geodesic paths. Euro. J. Appl. Math., 27:846–887, 2016.

>>> import cpnet
>>> lrc = cpnet.LowRankCore()
>>> lrc.detect(G)
>>> pair_id = lrc.get_pair_id()
>>> coreness = lrc.get_coreness()

Note

• [ ] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect a single core-periphery pair.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

cpnet.Divisive module

class cpnet.Divisive.Divisive(num_runs=10)

Bases: CPAlgorithm

Divisive algorithm.

This algorithm partitions a network into communities using the Louvain algorithm. Then, it partitions each community into a core and a periphery using the BE algorithm. The quality of a community is computed by that equipped with the BE algorithm.

19. Kojaku and N. Masuda. Core-periphery structure requires something else in the network. New Journal of Physics, 20(4):43012, 2018

>>> import cpnet
>>> alg = cpnet.Divisive()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [x] weighted

• [ ] directed

• [x] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

cpnet.KM_ER module

class cpnet.KM_ER.KM_ER(num_runs=10)

Bases: CPAlgorithm

Kojaku-Masuda algorithm with the Erdos-Renyi random graph.

This algorithm finds multiple core-periphery pairs in networks.

19. Kojaku and N. Masuda. Finding multiple core-periphery pairs in network. Phys. Rev. 96(5):052313, 2017

>>> import cpnet
>>> alg = cpnet.KM_ER()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [x] weighted

• [ ] directed

• [x] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

significance()

cpnet.KM_config module

class cpnet.KM_config.KM_config(num_runs=10)

Bases: CPAlgorithm

Kojaku-Masuda algorithm with the configuration model.

This algorithm finds multiple core-periphery pairs in networks.

19. Kojaku and N. Masuda. Core-periphery structure requires something else in networks. New J. Phys. 2018

>>> import cpnet
>>> alg = cpnet.KM_config()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [x] weighted

• [ ] directed

• [x] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

significance()

cpnet.Lip module

class cpnet.Lip.Lip

Bases: CPAlgorithm

Lip’s algorithm.

19. 26. W.~ Lip. A fast algorithm for the discrete core/periphery bipartitioning problem. arXiv, pages 1102.5511, 2011.

>>> import cpnet
>>> alg = cpnet.Lip()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [ ] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

cpnet.MINRES module

class cpnet.MINRES.MINRES(num_runs=10)

Bases: CPAlgorithm

MINRES algorithm.

Boyd, J. P., Fitzgerald, W. J., Mahutga, M. C., & Smith, D. A. (2010). Computing continuous core/periphery structures for social relations data with MINRES/SVD. Social Networks, 32(2), 125–137. https://doi.org/10.1016/j.socnet.2009.09.003

>>> import cpnet
>>> alg = cpnet.MINRES()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [x] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [x] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

cpnet.Rombach module

class cpnet.Rombach.Rombach(num_runs=10, alpha=0.5, beta=0.8, algorithm='ls')

Bases: CPAlgorithm

Rombach’s algorithm for finding continuous core-periphery structure.

16. Rombach, M. A. Porter, J. H. Fowler, and P. J. Mucha. Core-Periphery Structure in Networks (Revisited). SIAM Review, 59(3):619–646, 2017

>>> import cpnet
>>> alg = cpnet.Rombach()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [x] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [x] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

class cpnet.Rombach.SimAlg(A, x, alpha, beta)

Bases: Annealer

corevector(x, alpha, beta)

energy()

Calculate state’s energy

eval(od)

move()

Swaps two nodes.

cpnet.Rossa module

class cpnet.Rossa.Rossa

Bases: CPAlgorithm

Rossa’s algorithm for finding continuous core-periphery structure.

This algorithm finds multiple core-periphery pairs in networks.

6. Rossa, F. Dercole, and C. Piccardi. Profiling core-periphery network structure by random walkers. Scientific Reports, 3, 1467, 2013

>>> import cpnet
>>> alg = cpnet.Rossa()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [x] weighted

• [x] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

cpnet.Surprise module

class cpnet.Surprise.Surprise(num_runs=10)

Bases: CPAlgorithm

Core-periphery detection by Surprise.

10. van Lidth de Jeude, G. Caldarelli, T. Squartini. Detecting Core-Periphery Structures by Surprise. EPL, 125, 2019

>>> import cpnet
>>> alg = cpnet.Surprise()
>>> alg.detect(G)
>>> pair_id = alg.get_pair_id()
>>> coreness = alg.get_coreness()

Note

• [ ] weighted

• [ ] directed

• [ ] multiple groups of core-periphery pairs

• [ ] continuous core-periphery structure

detect(G)

Detect core-periphery structure.

Parameters

G (networkx.Graph or scipy sparse matrix) – Graph

Returns

None

Return type

None

cpnet.adam module

class cpnet.adam.ADAM

Bases: object

update(theta, grad, lasso_penalty, positiveConstraint=False)

Ascending.

cpnet.qstest module

cpnet.qstest.config_model(G)

cpnet.qstest.erdos_renyi(G)

cpnet.qstest.qstest(pair_id, coreness, G, cpa, significance_level=0.05, null_model=<function config_model>, sfunc=<function sz_n>, num_of_rand_net=100, q_tilde=[], s_tilde=[], **params)

(q,s)-test for core-periphery structure.

Sadamori Kojaku and Naoki Masuda. A generalised significance test for individual communities in networks. Scientific Reports, 8:7351 (2018)

Parameters

• pair_id (dict) – node i belongs to pair pair_id[i]

• coreness (dict) – node i is a core (x[i]=1) or a periphery (x[i]=0)

• G (networkx.Graph or scipy sparse martix) – Network

• cpa (CPAlgorithm) – algorithm that detects the core-periphery structure in question

• significance_level (float, optional) – Significicance level, defaults to 0.05

• null_model (func, optional) – funcion to produce a null model, defaults to config_model

• sfunc (func, optional) – Size function that calculates the size of a community, defaults to sz_n

• num_of_thread (int, optional) – Number of threads, defaults to 4

• num_of_rand_net (int, optional) – Number of random networks, defaults to 300

• q_tilde (list, optional) – pre-computed sampled of strength q of core-periphery structure, defaults to []

• s_tilde (list, optional) – pre-computed sample of the size of a core-periphery pair, defaults to []

>>> import cpnet
>>> km = cpnet.KM_config()
>>> km.detect(G)
>>> pair_id = km.get_pair_id()
>>> coreness = km.get_coreness()
>>> sig_pair_id, sig_coreness, significance, p_values = cpnet.qstest(pair_id, coreness, G, km)

cpnet.qstest.sampling(G, cpa, sfunc, null_model)

cpnet.qstest.sz_degree(network, c, x)

cpnet.qstest.sz_n(network, c, x)

cpnet.utils module

cpnet.utils.calc_node_pos(G, layout_algorithm)

cpnet.utils.classify_nodes(G, c, x, max_num=None)

cpnet.utils.draw(G, c, x, ax, draw_edge=True, font_size=0, pos=None, cmap=None, max_group_num=None, draw_nodes_kwd={}, draw_edges_kwd={'edge_color': '#adadad'}, draw_labels_kwd={}, layout_algorithm=None)

Plot the core-periphery structure in the networks.

Parameters

• G (networkx.Graph) – Graph

• c (group membership c[i] of i) – dict

• x (dict) – core (x[i])=1 or periphery (x[i]=0)

• ax (matplotlib.pyplot.ax) – axis

• draw_edge (bool, optional) – whether to draw edges, defaults to True

• font_size (int, optional) – font size for node labels, defaults to 0

• pos (dict, optional) – pos[i] is the xy coordinate of node i, defaults to None

• cmap (matplotlib.cmap, optional) – colomap defaults to None

• max_group_num (int, optional) – Number of groups to color, defaults to None

• draw_nodes_kwd (dict, optional) – Parameter for networkx.draw_networkx_nodes, defaults to {}

• draw_edges_kwd (dict, optional) – Parameter for networkx.draw_networkx_edges, defaults to {“edge_color”: “#adadad”}

• draw_labels_kwd (dict, optional) – Parameter for networkx.draw_networkx_labels, defaults to {}

• layout_kwd (dict, optional) – layout keywords, defaults to {}

Returns

(ax, pos)

Return type

matplotlib.pyplot.ax, dict

cpnet.utils.draw_interactive(G, c, x, hover_text=None, node_size=10.0, pos=None, cmap=None)

cpnet.utils.set_node_colors(c, x, cmap, colored_nodes)

cpnet.utils.to_adjacency_matrix(net)

cpnet.utils.to_nxgraph(net)

Module contents