Characterization and control of small-world networks

Recently, Watts and Strogatz Nature (London) 393, 440 (1998) offered an interesting model of small-world networks. Here we concretize the concept of a "faraway" connection in a network by defining a far edge. Our definition is algorithmic and independent of any external parameters such as topology of the underlying space of the network. We show that it is possible to control the spread of an epidemic by using the knowledge of far edges. We also suggest a model for better product advertisement using the far edges. Our findings indicate that the number of far edges can be a good intrinsic parameter to characterize small-world phenomena.