Network evolution is a ubiquitous phenomenon in a wide variety of complex systems. There is an increasing interest in statistically modeling the evolution of complex networks such as small-world networks and scale-free networks. In this article, we address a practical issue concerning the visualization of network evolution. We compare the visualizations of co-citation networks of scientific publications derived by two widely known link reduction algorithms, namely minimum spanning trees (MSTs) and Pathfinder networks (PFNETs). Our primarily goal is to identify the strengths and weaknesses of the two methods in fulfilling the need for visualizing evolving networks. Two criteria are derived for assessing visualizations of evolving networks in terms of topological properties and dynamical properties. We examine the animated visualization models of the evolution of botulinum toxin research in terms of its co-citation structure across a 58-year span (1945-2002). The results suggest that although high-degree nodes dominate the structure of MST models, such structures can be inadequate in depicting the essence of how the network evolves because MST removes potentially significant links from high-order shortest paths. In contrast, PFNET models clearly demonstrate their superiority in maintaining the cohesiveness of some of the most pivotal paths, which in turn make the growth animation more predictable and interpretable. We suggest that the design of visualization and modeling tools for network evolution should take the cohesiveness of critical paths into account.