Dichotomy of the same entities by alternative network representations.

<p>Alternate representations of the same network can lead to different topologies, especially for networks with natural hierarchical organization. We illustrate this tendency for (a) the Internet and (b) the yeast cell proteome. Each can be modeled by networks at two different granularities, representing nodes either as upper level components (internet domains or protein processes) or lower level components (internet routers or individual proteins). For the internet, previous Internet mapping studies provide both a router-level network and a domain-level network [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121248#pone.0121248.ref024" target="_blank">24</a>]; each domain is composed on multiple routers, and domains are connected <i>via</i> between-domain routers. For the protein network, we defined protein processes by hierarchically clustering proteins based on their pairwise interactions as in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121248#pone.0121248.ref012" target="_blank">12</a>]. A total of 333 biological processes were defined and connections between processes were defined based on pairwise interactions between proteins within each process. The networks’ hierarchical structure was analyzed and plotted as in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121248#pone.0121248.g002" target="_blank">Fig. 2</a></b>, marking the mean clustering coefficient for each entire network as a horizontal solid line in the plot. The non-hierarchical router and protein networks generally exhibited clustering coefficients near this average regardless of node degree, although for the Internet router-level network, routers with >300 connections showed exceptionally low clustering coefficients primarily due to a small number of between-domain routers located at a few top-level domains of the Internet.