A BRIEF INTRODUCTION TO SCALE‐FREE NETWORKS

. This article provides a brief introduction to scale-free networks. The notion of a scale-free network is defined and some examples given. Properties frequently exhibited by scale-free networks are discussed. The importance of the phenomenon of preferential attachment in generating scale-free networks is illustrated with two examples for the spread of a persistent disease. The models are similar in that they both yield a total infected population (1) which is geometrically distributed, and growing exponentially in expectation; and (2) in which the average distance from the original source of infection grows in a similar way over time. However one model, which has preferential attachment (infection), yields a scale-free network, while the other which has homogeneous infectivity does not. The possible application of the theory of scale-free networks to resource management is briefly discussed.

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