  We investigate small-world networks from the point of view of their origin.
While the characteristics of small-world networks are now fairly well
understood, there is as yet no work on what drives the emergence of such a
network architecture. In situations such as neural or transportation networks,
where a physical distance between the nodes of the network exists, we study
whether the small-world topology arises as a consequence of a tradeoff between
maximal connectivity and minimal wiring. Using simulated annealing, we study
the properties of a randomly rewired network as the relative tradeoff between
wiring and connectivity is varied. When the network seeks to minimize wiring, a
regular graph results. At the other extreme, when connectivity is maximized, a
near random network is obtained. In the intermediate regime, a small-world
network is formed. However, unlike the model of Watts and Strogatz (Nature {\bf
393}, 440 (1998)), we find an alternate route to small-world behaviour through
the formation of hubs, small clusters where one vertex is connected to a large
number of neighbours.
