New quantitative measures of urban structural changes are introduced and applied to the fast-growing city of Kerman, Iran. The results of 20,802 street measurements show that the main street orientations are orthogonal, both in the old inner part and in the more recent outer parts, but the streets are shorter and more irregular in shape in the inner part. The Shannon/Gibbs entropy is a measure of dispersion and is used to quantify the street-population differences within Kerman. The results show that then inner (old) part has lower orientation and length entropies (and shorter average lengths and length ranges) than any of the outer parts. Also, the length entropy gradually increases with distance from the inner part, indicating spreading of the street network with expansion of the city. The evolution of the Kerman street network from 1902 to 2006 indicates two growth processes: densification (streets added within the existing network) and expansion (streets added at the margin of the network). During densification periods, the network entropy decreased, but it increased during expansion periods. Entropy is thus a powerful tool for quantifying the evolution of city structure and for understanding and planning structural changes, particularly in fast-growing cities.