Ecology and Topology in the Financial World – Part III

by Yaniv Altshuler

In the previous post we have shown the topology and money flow dynamics of the financial system in the U.S. This data, operated by the Federal Reserve System, represents approximately 9,500 participating banks transfer funds. The sample from this network amounted to around 700,000 transfers, with just over 5,000 banks involved on an average day.

We saw that when browsed from close distance, we can see that the structure of the “dominating core” of this system (namely, the group of banks and bankers controlling the major part of the money flow in the U.S) follows a strongly connected pattern. This connectivity is characterized by a relatively small number of strong flows (many transfers) between nodes, with the vast majority of linkages being weak to zero (few to no flows). On a daily basis, 75% of the payment flows involve fewer than 0.1% of the nodes, and only 0.3% of the observed linkages between nodes (which are already extremely sparse).

As pointed out by May et. Al., the topology of this Fedwire network is highly disassortative: namely, large banks were disproportionately connected to small banks, and the other way around. Although the average number of connection a bank has was 15, this does not give an accurate idea of the reality in which most banks have only a few connections while a small number of ‘hubs’ have thousands. We already saw similar structure when we discussed the connection between movie start, i.e. the Small World phenomenon, described in the following rule :


We can be seen in the Fedwire network is a different manifestation of the same principle, called the Power-Law principle (we will discuss this principle in great details in future posts). Indeed – the money flow network appears to be governed by a relatively small number of dominating actors. This is not that surprising for those familiar with network theory, as such a pattern can be expected if we (reasonably so) assume that this system follows a preferential attachment process (this process, often treated as “the rich get richer law” will be discussed in future posts).

These strongly nonrandom and disassortative characteristics of the bank-transfer network are shared by some ecological systems. They also resonate with theoretical studies suggesting that sparseness of strong linkages can confer greater stability in systems whose components (nodes, banks, species) have some self-regulation. More generally, ecologists and others have long suggested that modularity — the degree to which the nodes of a system can be decoupled into relatively discrete components — can promote robustness.

Understanding this basic principle, many examples for it can easily be found in a great variety of every day environments. In forests, for example, fires can quickly spread if the environment is highly connected. A solution to this is the creation of firebreaks trenches or roads. Another example is the spread of biological diseases, likely to become epidemics when strong interconnection among all elements exists and can be efficiently contained either through the vaccination ‘superspreaders’, or through manipulation in the interactions topology (preventing sick people to come to work, improving sanitary conditions in high perturbation places such as airports, etc.).

Diving deeper into the applicative aspects of this understanding, one may wonder how can this issue be mathematically resolved? How can we find the best strategy for monitoring (or manipulating) the interactions between individual traders, or bankers ? More on this, next time.