A Hybrid Graph-drawing Algorithm for Large, Naturally-clustered, Disconnected Graphs

In this paper, we present a hybrid graph-drawing algorithm (GDA) for layouting large, naturally-clustered, disconnected graphs. We called it a hybrid algorithm because it is an implementation of a series of already known graph-drawing and graph-theoretic procedures. We remedy in this hybrid the problematic nature of the current force-based GDA which has the inability to scale to large, naturally-clustered, and disconnected graphs. These kinds of graph usually model the complex inter-relationships among entities in social, biological, natural, and artificial networks. Obviously, the hybrid runs longer than the current GDAs. By using two extreme cases of graphs as inputs, we present in this paper the derivation of the time complexity of the hybrid which we found to be $O(\mathrm{\mid }\text{V}{\mathrm{\mid }}^3)$.