the dynamical structure of political corruption networks · the dynamical structure of political...
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The dynamical structure of political corruption networksLuiz GA Alves1,∗, Haroldo V Ribeiro2, Alvaro F Martins2, Ervin K Lenzi3, Matjaž Perc4,5
1University of São Paulo, 2State University of Maringá, 3State University of Ponta Grossa, 4University of Maribor, 5Complexity Science Hub
Abstract
Corruptive behaviour in politics limits economic growth, embezzles public funds and promotes socio-economic inequality in modern democracies. We analyse well-documented political corruption scandalsin Brazil over the past 27 years, focusing on the dynamical structure of networks where two individualsare connected if they were involved in the same scandal. Our research reveals that corruption runs insmall groups that rarely comprise more than eight people, in networks that have hubs and a modularstructure that encompasses more than one corruption scandal. We observe abrupt changes in the sizeof the largest connected component and in the degree distribution, which are due to the coalescence ofdifferent modules when new scandals come to light or when governments change. We show further thatthe dynamical structure of political corruption networks can be used for successfully predicting partnersin future scandals. We discuss the important role of network science in detecting and mitigating politicalcorruption.
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Corruption case
DCB
A
7.51 ± 0.03
1.2 ± 0.4
Figure 1: Demography and evolving behaviour of corruption scandals in Brazil. A) The number ofpeople involved in each corruption scandal in chronological order (from 1987 to 2014). B) Cumulativeprobability distribution (on a log-linear scale) of the number of people involved in each corruption scandal(red circles). C) Time series of the number of people involved in corruption scandals by year (red circles).The alternating gray shades indicate the term of each general election that took place in Brazil between1987 and 2017. D) Autocorrelation function of the time series of the yearly number of people involved inscandals (red circles).
Figure 2: Complex network representation of people involved in corruption scandals. Complex networkof people involved in all corruption cases in our dataset (from 1987 to 2014). Each vertex represents aperson and the edges among them occur when two individuals appear (at least once) in the same corruptionscandal. Node sizes are proportional to their degrees and the colour code refers to the modular structure ofthe network. There are 27 significant modules, and 14 of them are within the giant component (indicatedby the red dashed loop).
Figure 3: Characterization of nodes based on the within-module degree (Z) and participation coefficient(P ). Each dot in the Z-P plane corresponds to a person in the network and the different shaded regionsindicate the different roles according to the network cartography proposed by Guimerà and Amaral. Themajority of nodes (97.5%) are classified as ultraperipheral (R1) or peripheral (R2), and the remaining arenon-hub connectors (R3, three nodes), provincial hubs (R5, three nodes), and connector hubs (R6, twonodes).
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2.4 ± 0.1
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Figure 4: The vertex degree distribution is exponential, invariant over time, and the characteristic degreeexhibits abrupt changes over the years.
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Siz
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parabólica
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de obras em SP
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Year: 1998Year: 1997
Year: 2005Year: 2004
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Year: 1992
Year: 1991
Co
llor
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Figure 5: Changes in the size of the largest component of the corruption network over time are causedby a coalescence of network modules.
Fra
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Figure 6: Predicting missing links between people in the corruption network may be useful for investigat-ing and mitigating political corruption. We tested the predictive power of eleven methods for predictingmissing links in the corruption networks. These methods are based on local similarity measures (degreeproduct, association strength, cosine, Jaccard, resource allocation, Adamic-Adar, and common neighbours),global (path- and random walk-based) similarity measures (rooted PageRank and SimRank), and on thehierarchical structure of networks (hierarchical random graph – HRV). To access the accuracy of thesemethods, we applied each algorithm to snapshots of the corruption network in a given year (excluding2014), ranked the top-10 predictions, and verified whether these predictions appear in future snapshots ofthe network. The bar plot shows the fraction of correct predictions for each method. We also included thepredictions of a random model where missing links are predicted by chance (error bars are 95% bootstrapconfidence intervals).
Reference
• HV Ribeiro, LGA Alves, AF Martins, EK Lenzi, M Perc The dynamical structure of politicalcorruption networks, Journal of Complex Networks CNY002, 1-15 (2018). ∗[email protected]