Twitter is now a key platform for public communication between a diverse range of participants, but the overall shape of the communication network it provides remains largely unknown. This article provides a detailed overview of the network structure of the Australian Twittersphere and identifies the thematic drivers of the key clusters within the network. We identify some 3.72 million Australian Twitter accounts and map the follower/followee connections between the 255,000 most connected accounts; we utilize community detection algorithms to identify the major clusters within this network and examine their account populations to identify their constitutive themes; we examine account creation dates and reconstruct a timeline for the Twitter adoption process among different communities; and we examine lifetime and recent tweeting patterns to determine the historically and currently most active clusters in the network. In combination, this offers the first rigorous and comprehensive study of the network structure of an entire national Twittersphere.