We consider an idealized model in which individuals changing opinions and their social network coevolve, with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the disc
ordant edge. Specifically, an interaction between $x$ and one of its neighbors $y$ leads to $x$ imitating $y$ with probability $(1-alpha)$ and otherwise (i.e., with probability $alpha$) $x$ cutting its tie to $y$ in order to instead connect to a randomly chosen individual. Building on previous work about the two-opinion case, we study the multiple-opinion situation, finding that the model has infinitely many phase transitions. Moreover, the formulas describing the end states of these processes are remarkably simple when expressed as a function of $beta = alpha/(1-alpha)$.
We use techniques from network science to study correlations in the foreign exchange (FX) market over the period 1991--2008. We consider an FX market network in which each node represents an exchange rate and each weighted edge represents a time-depe
ndent correlation between the rates. To provide insights into the clustering of the exchange rate time series, we investigate dynamic communities in the network. We show that there is a relationship between an exchange rates functional role within the market and its position within its community and use a node-centric community analysis to track the time dynamics of this role. This reveals which exchange rates dominate the market at particular times and also identifies exchange rates that experienced significant changes in market role. We also use the community dynamics to uncover major structural changes that occurred in the FX market. Our techniques are general and will be similarly useful for investigating correlations in other markets.
