Small Worlds
One of the most cited results in the cascade literature is the effect of random perturbations, or 'bridge ties', on the propagation rates of cascades. The classic paper is by Duncan Watts and Steven Strogatz.
Small Worlds
In a follow-up paper, Watts explores the implications of these results for a sociological audience.
Watts on Networks
Recent work by Centola, Macy and Eguiluz extends this work by showing how contagions that have non-trivial thresholds, such as riots, herding behaivor, and social movemnts, will propagate more slowly - and in some cases fail to propagate at all - as bridge ties are added to a regular lattice.
Multiplex Propagation
Mark Newman and Christopher Moore develop a percolation model for the spread of an epidemic on a small worlds network.
Epidemic Percolation Model
Random Networks
Watts gives a very nice treatment of the general properties of cascades on random networks.
Watts Random Network
Barabasi and his colleagues showed that the world wide web is a random network that exhibits a scale-free degree distribution.
Random Scale Free Topology
They then went on to demonstrate important properties of these networks for both attacks and errors.
Network Robustness
Network Structure
Mark Newman and Michelle Girvan present a model for detecting community structure in networks.
Community Structure
This study tries to detect regular structures in the self-organization of the world wide web.
World Wide Web Structure
