The document summarizes a research conference presentation on using Google's PageRank algorithm and variants to analyze centrality and flows within networks. The presentation discussed applying these methods to analyze world trade networks and commodities trade between countries. It also considered whether these network analysis techniques could help measure systemic importance within the financial system and identify institutions that are too interconnected fail. The presentation concluded by encouraging further applications of these Google matrix methods to investigate various economic flows and networks.

1. 14th Annual DNB Research Conference
2-4 November 2011
Discussion of
“Google matrix of the world trade network”
by L. Ermann and D.L .Shepelyansky
Kimmo Soramäki
www.fna.fi

2. The paper
• Investigates the properties of a particular centrality measure -
Pagerank
• And its applicability in describing nodes in commodities trade
networks
• Ties in with research developed in parallel in matrix theory,
physics, sociology, computer science
• Question today: can the approach could be used for banking
networks

3. Common centrality measures
Degree: number of links
Closeness: distance to other
nodes via shortest paths
Betweenness: number of shortest
paths going through the node
Eigenvector: nodes that are linked by
other important nodes are more central,
probability of a random process

4. Centrality depends on
network process
Trajectory geodesic paths, paths, trails or walks
Transmission parallel/serial duplication or transfer
Source: Borgatti (2004)
4

5. Problem with EV centrality
It can be (meaningfully) calculated only for “Giant Strongly
Connected Component” (GSCC)
Random process would
end at GOUT (dangling
links, dead-ends)

6. Pagerank solves this with
“damping factor”
• Damping factor
– Gi,j= Si,j
– complete symmetric network
– EV centrality
• Original story: Web surfer will go to a random page
after surfing to a page without outbound links
-> How good of a story for other processes,
such as trade?

7. How about bipartite networks
• Bipartite networks have links between two types of nodes
(call them exporters and importers)
• Are countries in mainly exporter or importers? Does
it work better for more complex products.
• How much are the results driven by
the damping factor?
• How much more information does
Pagerank or Cheirank bring?

8. All commodities
PageRank CheiRank ImportRank ExportRank

9. Barley
PageRank CheiRank ImportRank ExportRank

10. Use it for financial stability?
• Mostly interested in contagion process, high policy interest for
measures of systemic importance
• Quite a number of empirical papers on financial systems that look at
different metrics
– Interbank payments: Soramäki et al (2006), Becher et al. (2008), Boss et al.
(2008), Pröpper et al. (2009), Embree and Roberts (2009), Akram and
Christophersen (2010) …
– Overnight loans: Atalay and Bech (2008), Bech and Bonde (2009), Wetherilt et
al. (2009), Iori et al. (2008) and Heijmans et al. (2010), Craig & von Peter
(2010) …
– Flow of funds, Credit registry, Stock trading…: Castren and Kavonius (2009),
Bastos e Santos and Cont (2010), Garrett et al. 2011, Minoiu and Reyes (2011),
(Adamic et al. 2009, Jiang and Zhou 2011) …
– More at www.fna.fi/blog

11. Interpretation for financial stability
• Similar process as payments (transfer), not so sure about
counterparty risk (parallel duplication)
• Closest to Bech-Chapman-Garratt (2008)
– “Which Bank Is the “Central” Bank? An Application of Markov Theory to the
Canadian Large Value Transfer System”
• Page/Cheirank as systemic importance/ vulnerability?
– “too interconnected to fail”
• What is the theory, what is the process in the network?
– Contagion models? Cascading failures models?
• How to test it?
– Regressions? Simulations that emulate the process? Agent-based models?

12. The paper ends with:
“We hope that this new approach based on the
Google matrix will find further useful applications
to investigation of various flows in trade
and economy.”

13. Try it with some BIS statistics
• Nodes
– Countries that have out and inbound links reported
– Consider GSCC only
• Links
– National banking systems' on-balance sheet financial claims by country
– Table 9D, “Foreign claims by nationality of reporting banks, ultimate risk
basis”
• Look at damping factor and Page/Cheirank plane
Has claim from
A B
Owes money to

14. Alpha 1 (left) and 0.85 (right)

15. Alpha 0.5 (left) and 0 (right)

16. Pagerank vs Cheirank

17. Page vs Cheirank
Systemically important Systemically important and vulnerable
Systemically vulnerable

18. Thank you