Distance Closure on Complex Networks

# Distance Closure on Complex Networks (Network Backbone)

## Description

This package implements methods to calculate the Distance Closure of Complex Networks including its Metric and UltraMetric Backbone.

## Installation

Latest development release on GitHub (v0.5):

pip install git+https://github.com/CASCI-lab/distanceclosure


Latest PyPI stable release (v0.4.1):

\$pip install distanceclosure


## Simple usage

How to calculate Closure of a weighted distance graph:

    import networkx as nx
import distanceclosure as dc

# Instanciate a (weighted) graph
edgelist = {
('s', 'a'): 8,
('s', 'c'): 6,
('s', 'd'): 5,
('a', 'd'): 2,
('a', 'e'): 1,
('b', 'e'): 6,
('c', 'd'): 3,
('c', 'f'): 9,
('d', 'f'): 4,
('e', 'g'): 4,
('f', 'g'): 0,
}
G = nx.from_edgelist(edgelist)
# Make sure every edge has an attribute with the distance value
nx.set_edge_attributes(G, name='distance', values=edgelist)

# Compute closure (note this will be a fully connected graph for an undirected connected component. It can be slow for large graphs)
C = dc.distance_closure(G, kind='metric', weight='distance')

# You can now access the new metric_distance value and whether the edge is part of the metric backbone.
C['s']['c']
> {'distance': 6, 'metric_distance': 6, 'is_metric': True}


If you are only interested in the metric backbone itself:

    B = dc.metric_backbone(G, weight='distance')

B.number_of_edges()
> 9
C.number_of_edges()
> 28
G.number_of_edges()
> 11


## Papers

• F.X. Costa, R.B. Correia, L.M. Rocha [2023]. "The distance backbone of directed networks". In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. doi: 10.1007/978-3-031-21131-7_11

• T. Simas, R.B. Correia, L.M. Rocha [2021]. "The distance backbone of complex networks". Journal of Complex Networks, 9 (6):cnab021. doi: 10.1093/comnet/cnab021

• T. Simas and L.M. Rocha [2015]."Distance Closures on Complex Networks". Network Science, 3(2):227-268. doi:10.1017/nws.2015.11

## Credits

distanceclosure was originally written by Rion Brattig Correia with input from many others. Thanks to everyone who has improved distanceclosure by contributing code, bug reports (and fixes), documentation, and input on design, and features.

## Support

Those who have contributed to distanceclosure have received support throughout the years from a variety of sources. We list them below.

• CASCI, Binghamton University, Binghamton, NY; PI: Luis M. Rocha
• CAPES Foundation, Ministry of Education of Brazil, Brasília, Brazil; Rion B. Correia.

## Development

Pull requests are welcome :) Please get in touch beforehand: rionbr(at)gmail(dot)com or fcosta(at)binghamton(dot)edu.

## Changelog

v0.5

• Iterative backbone computation (faster for graphs with smaller backbones)

v0.4

• Code simplification and compliance to NetworkX

v0.3.6

• Dijkstra Cythonized

v0.3.2

• S and B measure added to closure

v0.3.0

• Dijkstra APSP algorithm
• Support for sparse matrices

v0.2

• First docs released

v0.1

• First release nad dense matrix APSP

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