BioGrapher: visualization of graph theoretical patterns, measurements, and analysis in mathematical biology. Graph theory provides mathematical insight into many areas of contemporary biology such as genomics, metabolonomics, ecology, evolution, biochemistry, etc. because it provides a highly visual and easily comprehensible representation of patterns, processes, and products for testing causal hypotheses. Thus, there is an enormous need for graph theoretic visualization tools that make it easy for biologists to enter data, interact with existing data bases, and generate a variety of different layouts of graphs. BioGrapher is a versatile Excel front-end for the Graphviz graphical visualization library and software package that we have contributed to the Biological Excel Simulations and Tools for Exploratory, Experiential Mathematics (ESTEEM) collection, available online at url{}. While a number of excellent stand-alone applications that incorporate Graphviz for different platforms and operating systems are available, BioGrapher is unique in that, in keeping with the best practices standards of the ESTEEM suite of which it is a part, it uses the standard and ubiquitous Excel environment as the front-end and graphical user interface. It implements the visualization of graphs (nodes and edges) that are specified as standard adjacency matrices using the Excel spreadsheet paradigm of rows and columns, with connections between nodes represented by a non-zero (non-empty) cell value for the appropriate row and column. A complete Visual Basic for Applications (VBA) Excel interface has been programmed and implemented as an additional custom menu bar menu, with enough functionality for the user to invoke many graphical drawing and manipulation routines. Herein we present details of the Excel app (available for both MacOS X and MS Windows 7/8) and its applications in problem solving in mathematical biology. Specifically, we present details for food webs as canonical examples of biological networks that may display the properties and features associated with small world networks. An algorithmic approach using graph theory, BioGrapher, and the complementary JavaBENZER app for generation of interval graphs is demonstrated.