Complex Networks

by Yaniv Altshuler

In the previous post, I have presented the general concept of “networks”, and discussed their broad use in a great variety of scientific domains, due to their high flexibility, that enables network to be used as a basic building block in many model or more complicated analytic structures. This flexibility, however, may sometime baffle the novice researcher, as different types of networks may present very different kinds of behaviors and properties.

At this point, when analyzing social trading networks such as OpenBook, it would be useful to take a step back and observe the layout, or configuration, of said network, remembering the functional role of each of its elements. Specifically, note that out basic units, or nodes, correspond to the people, or traders, that use our trading network. As such, further assumption concerning the network’s composition can be made, that normally take place while observing human behavior. One such assumption is that people usually have a limited number of social or professional relationships. That is, whereas a person with 5,000 friends on Facebook may exist, the average (and most frequent) number of social connections is much smaller.

Another slightly less intuitive observation is the fact that human form social relationships which are seldom random. That is, the basic structure that is formed by human interactions follows certain patterns, or regularity. This fact, although may seem trivial or mundane, encapsulates a great deal of insights that can be drawn with respect to the analysis of trading networks. For example – knowing a trader’s preferences with respect to the various trading tools offered by the system, highly probable estimations concerning her social preferences could be made. Alternatively, having access to the trading network structure (or topology), a person’s likelihood to use high leverage trading (or take other risks) can be approximated.

In this sense, social trading networks belong to a unique family of networks, called “Complex Networks” – networks with that has non-trivial topological features. That is, networks that span some composition of rules that together yield a structure that is not random on one hand, yet of no perfect regularity on the other. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks such as social and communication networks.

Understanding social networks opens way to the development of potent analytic and predictive methods that can successfully be applied to a variety of domains. Due to the importance of complex networks, I will dedicate the next posts for a more detailed discussion of two specific sub-classes of complex networks and their interesting and useful properties.