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Network Controllability Metrics for Corruption Research

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Abstract

This chapter will discuss political corruption in a legislative social network using the tools of network control theory. We aim to cultivate an understanding of the mechanisms by which corrupting actors can perturb nodes’ behavior at certain points within a larger social system, and harness the natural magnification of these perturbations to drive the network to a more desirable state. In other words, we investigate how social capital is harnessed to amplify the effects of corruption using a social influence network or hierarchy. We provide a brief overview of control-theoretic metrics that may prove useful to researchers in identifying high-risk areas of legislative or other political social networks—areas which are particularly vulnerable to the spread of misinformation, and thus particularly valuable to the corruption of social dynamics.

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Fig. 3.1
Fig. 3.2
Fig. 3.3
Fig. 3.4

Notes

  1. 1.

    The fact that in the best-response dynamics, players do not take into account how others in the network will update their opinions in each round is what makes these dynamics myopic or naïve.

  2. 2.

    The geometric multiplicity of an eigenvalue is the rank of its associated eigenspace, or the number of linearly independent eigenvectors it is associated with. If the network matrix A is diagonalizable (which is the case if the network is undirected), then the geometric multiplicities of eigenvalues are equal to their algebraic multiplicities, or the number of times they appear as a root of the characteristic polynomial.

  3. 3.

    Algorithms for finding maximum matchings in a bipartite graph are well-established. For more information and a comprehensive overview of algorithms for finding maximum bipartite matchings, see [24].

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Acknowledgements

I would like to thank participants at the corruption networks satellite of NetSci2020 for helpful comments and advice. Thanks also to the Charles & Persis Rockwood Fellowship and the L. Charles Hilton Center for their generous support.

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Correspondence to Philip C. Solimine .

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Solimine, P.C. (2021). Network Controllability Metrics for Corruption Research. In: Granados, O.M., Nicolás-Carlock, J.R. (eds) Corruption Networks. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-81484-7_3

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