Network Theory and Financial Risk (2nd edition)
First published:
ISBN: 978-1-78272-432-2
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Brass tacks: Complexity reduction
Brass tacks: Complexity reduction
Preface
Acknowledgements
An introduction to financial networks
Creating and describing networks
Identifying important nodes: Centrality metrics
Uncovering latent structure: Clustering and community detection
Finding hidden links: Projection networks
Estimating unknown links: Network reconstruction
Fast insights: Visualising networks
Financial cartography: Network layouts
Brass tacks: Complexity reduction
Financial stability and systemic risk
Design and simulation of financial market infrastructures
Monitoring and stress testing financial market infrastructures
Financial crime and conduct risk
Financial markets
References
When networks get large, particularly in terms of the number of links, making sense of them becomes difficult. This chapter presents several methods for reducing the number of nodes or links in a network, leaving only the most important ones to create a subset of the original network that highlights important relationships and can be visualised more easily. Here we cover complexity reduction algorithms, focusing on threshold methods, spanning trees and planar maximally filtered graphs.
THRESHOLD METHODS
The simplest way to filter nodes or links from a network is by removing those whose property values are larger or smaller than some threshold. Depending on the use case, the threshold may be chosen as some intrinsically meaningful value. Network visualisations may allow for interactive filtering, allowing the user to choose a threshold such that the resulting network visualisation is appropriately uncluttered and easy to read, and also to observe how the network changes as the threshold changes. Alternatively, a threshold may be set such that a fixed number or proportion of nodes/links or node/link values is retained in the network. For example, the projection networks shown
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