Visualization of Complete Graphs, Trees and Series-Parallel Graphs for Practical Applications

Obtaining a comprehensive visualization of complete graphs, complete multipartite graphs and their homeomorphics has become a critical issue in many practical applications nowadays. Existing algorithms for drawing such graphs either impose restrictions on the number of vertices or use intricate mathematical concepts that make the drawing less comprehensive. Moreover, they are incapable of depicting the attributes of vertices and edges, which is often a requirement. In this paper, we present two 3D graph drawing conventions which can overcome these problems. We also show that it is possible in our convention to draw trees and series-parallel graphs with volume bounds of O(kn) and O(n² log n) respectively, where k is the maximum degree of any vertex in the tree.