We present Phylogenetic Graph (PhyG), an open-source, phylogenetic search tool for diverse data types and graphs, including softwired and hardwired networks, in addition to trees. This allows for analysis of horizontal transfer and hybridization scenarios, as well as the necessary vertical inheritance of trees. PhyG is the successor to POY5 in performing combined data tree-alignment with enhancements in heuristic optimality (up to 7% in example data) and execution time (up to a factor of 200). Input data may exhibit a practically unlimited number of character states in qualitative or sequence (aligned and unaligned) types. Novel graph construction and refinement algorithms have been implemented and integrated into a variety of search procedures. Currently, PhyG implements parsimony and No-Common-Mechanism Likelihood optimization.