The paper (Survival of the sparsest: robust gene networks are parsimonious) cited in that wikipedia article answers the question
This indicates that sparse networks are actually more robust if the costs of complexity are accounted for. If true, then evolution should seek to optimize the costs and benefits of complexity with a parsimonious network structure, a network topology that is sparsely connected and not unnecessarily complex, by seeking an optimal topological ensemble of interactions that best meets the network's functional requirements under its normal range of operating conditions.
When getting information from wikipedia it's always a good idea to read through the citations.
They are not only sparse, according to Barabasi work it's beleived they are also "scale-free", meaning the degree of nodes distribution follows a power law function. Then a lot of nodes have a low connectivity, and some have a high connectivity (they are called "hubs" or "modules").
Here is a review (to start): Barabási and Oltvai. Network biology: understanding the cell's functional organization. Nat Rev Genet (2004) vol. 5 (2) pp. 101-13