Networks

by Yaniv Altshuler

Previously, I have mentioned several times the term Trading Network. At first glance this term me intuitively seem self explanatory, as when asked to define it, most people would likely depict it as a “network” (in the sense of a group of people, or a service), that is used for the purpose of financial trading. However, in order to continue with our methodological understanding of social trading, we should formally understand what a “trading network” is. Whereas its second half (i.e. “trading”) describes the functional purpose of the term, its first has is associated with one of the most fundamental aspects in current research – networks.

Networks (or Graphs) are a specific case of systems that are pivotal in the analysis and understanding of social and financial communities. In general, networks are mathematical structured that can be defined as a collection of vertices (or nodes) and edges (or links), that may be directional or unidirectional, and may also have additional properties such as weight or capacity. Using this fairly simple structure, a huge variety of structures can be composed, making networks among the most ubiquitous models of both natural and human-made structures. They can be used to model many types of relations and process dynamics in physical, biological and social systems.

An example of a network of 6 nodes, marked 1 to 6, whereas node 1 is connected to node 4, node 4 is connected to nodes 3 and 5, and so on. Notice that this picture assumes an undirected network.

Among the many uses of networks as mathematical structures are the representation of communication networks, data organization or the flow of computation. One practical example is the representation of relations between websites as a directed graph, using which “central websites” can be detected (as done for example by Google’s PageRank algorithm).


An illustration of the PageRanks algorithm for a simple network. Each sphere (or node) represents a different website, and the arrows (or links) represent directed web links between the websites. A web surfer who chooses a random link on every page (but with 15% likelihood jumps to a random page on the whole web) is going to be on Page E for 8.1% of the time.

The same approach can be used for modeling a trading network, having nodes that represent the various traders, and connections that represent links between them (such as the “follow” link in the OpenBook platform). Measuring the probability distribution of traders to browse between the portfolios of the traders they follow, a “social score” for each trader can be calculated. A similar approach can be taken to problems in travel, biology, computer chip design, and many other fields. The development of algorithms to handle networks is therefore of major interest.

An interesting and unique type of networks is called Complex Networks, and will be presented next.