  Urban transportation systems grow over time as city populations grow and move
and their transportation needs evolve. Typical network growth models, such as
preferential attachment, grow the network node by node whereas rail and metro
systems grow by adding entire lines with all their nodes. The objective of this
paper is to see if any canonical regular network forms such as stars or grids
capture the growth patterns of urban metro systems for which we have historical
data in terms of old maps. Data from these maps reveal that the systems'
Pearson degree correlation grows increasingly from initially negative values
toward positive values over time and in some cases becomes decidedly positive.
We have derived closed form expressions for degree correlation and clustering
coefficient for a variety of canonical forms that might be similar to metro
systems. Of all those examined, only a few types patterned after a wide area
network (WAN) with a "core-periphery" structure show similar positive-trending
degree correlation as network size increases. This suggests that large metro
systems either are designed or evolve into the equivalent of message carriers
that seek to balance travel between arbitrary node-destination pairs with
avoidance of congestion in the central regions of the network.
  Keywords: metro, subway, urban transport networks, degree correlation
