Neglected tropical diseases, especially those caused by helminths, constitute some of the most common infections of the world's poorest people. Amongst these, schistosomiasis (bilharzia or 'snail fever'), caused by blood flukes of the genus Schistosoma, ranks second only to malaria in terms of human impact: two hundred million people are infected and close to 800 million are at risk of infection. Drug screening against helminths poses unique challenges: the parasite cannot be cloned and is difficult to target using gene knockouts or RNAi. Consequently, both lead identification and validation involve phenotypic screening, where parasites are exposed to compounds whose effects are determined through the analysis of the ensuing phenotypic responses. The efficacy of leads thus identified derives from one or more or even unknown molecular mechanisms of action. The two most immediate and significant challenges that confront the state-of-the-art in this area are: the development of automated and quantitative phenotypic screening techniques and the mapping and quantitative characterization of the totality of phenotypic responses of the parasite. In this paper, we investigate and propose solutions for the latter problem in terms of the following: (1) mathematical formulation and algorithms that allow rigorous representation of the phenotypic response space of the parasite, (2) application of graph-theoretic and network analysis techniques for quantitative modeling and characterization of the phenotypic space, and (3) application of the aforementioned methodology to analyze the phenotypic space of S. mansoni - one of the etiological agents of schistosomiasis, induced by compounds that target its polo-like kinase 1 (PLK 1) gene - a recently validated drug target. In our approach, first, bio-image analysis algorithms are used to quantify the phenotypic responses of different drugs. Next, these responses are linearly mapped into a low- dimensional space using Principle Component Analysis (PCA). The phenotype space is modeled using neighborhood graphs which are used to represent the similarity amongst the phenotypes. These graphs are characterized and explored using network analysis algorithms. We present a number of results related to both the nature of the phenotypic space of the S. mansoni parasite as well as algorithmic issues encountered in constructing and analyzing the phenotypic-response space. In particular, the phenotype distribution of the parasite was found to have a distinct shape and topology. We have also quantitatively characterized the phenotypic space by varying critical model parameters. Finally, these maps of the phenotype space allows visualization and reasoning about complex relationships between putative drugs and their system-wide effects and can serve as a highly efficient paradigm for assimilating and unifying information from phenotypic screens both during lead identification and lead optimization.