Feeds:
Posts

## Watts 2004: Structure of a network has large implications on dynamics on it

Global financial volatility follows dynamical laws on a large dense complex network with nodes equal the number of assets and therefore it is reasonable to expect that the observations of Watts and Strogatz from 2004 (and earlier) that the dynamics is affected by the graph topology applies and our expectation is that this topology is captured by fractional differential equations of the type

$(\partial_t^{\alpha} - (\Delta_G)^{\beta}) u = F(u)$

$u(0,x)=f(x)$

where the topology is captured by the Laplacian operator $\Delta_G$.

Watts_2004

This new network science has gone down the path of scale-free networks which are networks where the degree distribution follows a power law which is not observed in a typical financial network constructed using volatility correlations.