Concentric network symmetry

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Concentric network symmetry. / Silva, Filipi N.; Comin, César H.; DM. Peron, Thomas K.; Rodrigues, Francisco A.; Ye, Cheng; Wilson, Richard C.; Hancock, Edwin; da F. Costa, Luciano.

In: Information Sciences, Vol. 333, 10.03.2016, p. 61-80.

Research output: Contribution to journalArticlepeer-review

Harvard

Silva, FN, Comin, CH, DM. Peron, TK, Rodrigues, FA, Ye, C, Wilson, RC, Hancock, E & da F. Costa, L 2016, 'Concentric network symmetry', Information Sciences, vol. 333, pp. 61-80. https://doi.org/10.1016/j.ins.2015.11.014

APA

Silva, F. N., Comin, C. H., DM. Peron, T. K., Rodrigues, F. A., Ye, C., Wilson, R. C., Hancock, E., & da F. Costa, L. (2016). Concentric network symmetry. Information Sciences, 333, 61-80. https://doi.org/10.1016/j.ins.2015.11.014

Vancouver

Silva FN, Comin CH, DM. Peron TK, Rodrigues FA, Ye C, Wilson RC et al. Concentric network symmetry. Information Sciences. 2016 Mar 10;333:61-80. https://doi.org/10.1016/j.ins.2015.11.014

Author

Silva, Filipi N. ; Comin, César H. ; DM. Peron, Thomas K. ; Rodrigues, Francisco A. ; Ye, Cheng ; Wilson, Richard C. ; Hancock, Edwin ; da F. Costa, Luciano. / Concentric network symmetry. In: Information Sciences. 2016 ; Vol. 333. pp. 61-80.

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@article{44f0432ae2ac47eca9b038b661ac8ca6,
title = "Concentric network symmetry",
abstract = "Abstract Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify the symmetries around nodes, which we call connectivity patterns. We develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models, namely the Erd{\H o}s–R{\'e}nyi, Barab{\'a}si–Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi. Real-world networks, namely the scientific areas of Wikipedia, the world-wide airport network and the street networks of Oldenburg and San Joaquin, are also analyzed in terms of the proposed symmetry measurements. Several interesting results emerge from this analysis, including the high symmetry exhibited by the Erd{\H o}s–R{\'e}nyi model. Additionally, we found that the proposed measurements present low correlation with other traditional metrics, such as node degree and betweenness centrality. Principal component analysis is used to combine all the results, revealing that the concepts presented here have substantial potential to also characterize networks at a global scale. We also provide a real-world application to the financial market network.",
keywords = "Symmetry, Complex networks, Concentric, Measurements",
author = "Silva, {Filipi N.} and Comin, {C{\'e}sar H.} and {DM. Peron}, {Thomas K.} and Rodrigues, {Francisco A.} and Cheng Ye and Wilson, {Richard C.} and Edwin Hancock and {da F. Costa}, Luciano",
year = "2016",
month = mar,
day = "10",
doi = "10.1016/j.ins.2015.11.014",
language = "English",
volume = "333",
pages = "61--80",
journal = "Information Sciences",
issn = "0020-0255",
publisher = "Elsevier Inc.",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Concentric network symmetry

AU - Silva, Filipi N.

AU - Comin, César H.

AU - DM. Peron, Thomas K.

AU - Rodrigues, Francisco A.

AU - Ye, Cheng

AU - Wilson, Richard C.

AU - Hancock, Edwin

AU - da F. Costa, Luciano

PY - 2016/3/10

Y1 - 2016/3/10

N2 - Abstract Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify the symmetries around nodes, which we call connectivity patterns. We develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models, namely the Erdős–Rényi, Barabási–Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi. Real-world networks, namely the scientific areas of Wikipedia, the world-wide airport network and the street networks of Oldenburg and San Joaquin, are also analyzed in terms of the proposed symmetry measurements. Several interesting results emerge from this analysis, including the high symmetry exhibited by the Erdős–Rényi model. Additionally, we found that the proposed measurements present low correlation with other traditional metrics, such as node degree and betweenness centrality. Principal component analysis is used to combine all the results, revealing that the concepts presented here have substantial potential to also characterize networks at a global scale. We also provide a real-world application to the financial market network.

AB - Abstract Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify the symmetries around nodes, which we call connectivity patterns. We develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models, namely the Erdős–Rényi, Barabási–Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi. Real-world networks, namely the scientific areas of Wikipedia, the world-wide airport network and the street networks of Oldenburg and San Joaquin, are also analyzed in terms of the proposed symmetry measurements. Several interesting results emerge from this analysis, including the high symmetry exhibited by the Erdős–Rényi model. Additionally, we found that the proposed measurements present low correlation with other traditional metrics, such as node degree and betweenness centrality. Principal component analysis is used to combine all the results, revealing that the concepts presented here have substantial potential to also characterize networks at a global scale. We also provide a real-world application to the financial market network.

KW - Symmetry

KW - Complex networks

KW - Concentric

KW - Measurements

U2 - 10.1016/j.ins.2015.11.014

DO - 10.1016/j.ins.2015.11.014

M3 - Article

VL - 333

SP - 61

EP - 80

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

ER -