Package: network-symmetry
Network symmetryFast library, written in C for python to calculate network Accessibility and Symmetry. More information regarding these measurements are described in the papers listed as follows:TravenÃ§olo, Bruno Augusto Nassif, and L. da F. Costa. "Accessibility in complex networks." Physics Letters A 373, no. 1 (2008): 89-95.Silva, Filipi N., Cesar H. Comin, Thomas K. DM Peron, Francisco A. Rodrigues, Cheng Ye, Richard C. Wilson, Edwin R. Hancock, and Luciano da F. Costa. "Concentric network symmetry." Information Sciences 333 (2016): 61-80.For the generalized accessibility, the following paper is used:De Arruda, G. F., Barbieri, A. L., Rodriguez, P. M., Rodrigues, F. A., Moreno, Y., & da Fontoura Costa, L. Role of centrality for the identification of influential spreaders in complex networks. Physical Review E, 90(3) (2014), 032812.If you use this code in a scientific study, please cite the respective references and this library.A comprehensive guide to the theory and applications of the accessibility measurements is available from:Benatti, Alexandre, and Luciano da F. Costa. "Accessibility: Generalizing the Node Degree (A Tutorial)." (2021).InstallRequires python headers and a C11 compatible compiler, such as gcc or clang.To install it, simply run:pipinstallnetwork-symmetryor clone this repository and install it from master by running:pipinstallgit+https://github.com/ABenatti/network_symmetry.gitUsageStep 1: Import the librariesimportnumpyasnpimportnetwork_symmetryasnsStep 2: Convert network to an edge list and a list of weights (optional)vertex_count=10edges=np.array([(0,1),(0,2),(1,2),(0,3),(1,3),(2,3),(2,4),(3,4),(0,4),(4,5),(3,5),(1,5),(1,6),(3,6),(4,6),(5,7),(4,7),(0,7),(5,8),(4,8),(3,8),(3,9),(7,9),(0,9)])weights=np.random.random(size=edges.shape[0])directed=FalseStep 3: Load the network data in a measurer objectmeasurer=ns.Network(vertex_count=vertex_count,edges=edges,directed=directed,weights=weights)Step 4: Set the parameters:h_max=3measurer.set_parameters(h_max=h_max)Step 5: Calculate the measurements:measurer.compute_symmetry()generalized_accessibility=measurer.accessibility_generalized()Step 6: The outputs can be seen as follows.print("\nResults:")forhinrange(2,h_max+1):print("h =",h)print(" Accessibility:")print(" ",measurer.accessibility(h))print(" Symmetry (backbone):")print(" ",measurer.symmetry_backbone(h))print(" Symmetry (merged):")print(" ",measurer.symmetry_merged(h))print(" Generalized accessibility:")print(" ",generalized_accessibility)Important:In order to be faster, this version of accessibility considers a random walk in which the walker cannot return to the already visited nodes.API Documentationmeasurer=ns.Network(vertex_count=vertex_count,edges=edges,directed=directed,weights=weights)vertex_count- number of vertices in the network;edges- list of edges;directed- directed or not;weights- list containing the weights of the edges (use the same order as edges).measurer.set_parameters(h_max=2,merge_last_level=True,live_stream=False,parallel_jobs=1,verbose=False,show_status=True)h_max- Compute all symmetries and accessibilities for h=2 to h_max, which must be greater or equal to 2;merge_last_level- Merge the last level. True by default;live_stream- Stream the output as results are obtained. Note that the results may be out of order;parallel_jobs- The number of parallel jobs, which must be greater or equal to 1;verbose- If True, shows the calculation steps;show_status- If True, show the progress of the calculation.measurer.compute_symmetry()Compute symmetries and accessibilities by using the parameters set in "set_parameters".accessibility=measurer.accessibility(h)symmetry_backbone=measurer.symmetry_backbone(h)symmetry_merged=measurer.symmetry_merged(h)h- desired number of steps.
These methods return the respective lists measurements. The order of measures in the lists follows the node orders.LibrariesAll of these codes were developed and executed with the environment described in "requirements.txt".Citation RequestIf you publish a paper related to this material, please cite this repository and the respective papers.AcknowledgementsAlexandre Benatti thanks CoordenaÃ§Ã£o de AperfeiÃ§oamento de Pessoal de NÃ­vel Superior â€“ Brasil (CAPES) â€“ Finance Code (001) (grant no. 88882.328749/2019-01). Henrique F. de Arruda acknowledges FAPESP for sponsorship (grant no. 2018/10489-0). Luciano da F. Costa thanks CNPq (grant no. 307085/2018-0) and NAP-PRP-USP for sponsorship. This work has been supported also by FAPESP grant no. 2015/22308-2.LicenseThis software is under the following license.Copyright (c) 2021 network-accessibility

network-accessibility (c) by Alexandre Benatti, Henrique Ferraz de Arruda
Filipi Nascimento Silva, and Luciano da Fontoura Costa

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