Network models of healthcare systems can be used to examine how providers collaborate, communicate, refer patients to each other. Most healthcare service network models have been constructed from patient claims data, using billing claims to link patients with providers. The data sets can be quite large, making standard methods for network construction computationally challenging and thus requiring the use of alternate construction algorithms. While these alternate methods have seen increasing use in generating healthcare networks, there is little to no literature comparing the differences in the structural properties of the generated networks. To address this issue, we compared the properties of healthcare networks constructed using different algorithms and the 2013 Medicare Part B outpatient claims data. Three different algorithms were compared: binning, sliding frame, and trace-route. Unipartite networks linking either providers or healthcare organizations by shared patients were built using each method. We found that each algorithm produced networks with substantially different topological properties. Provider networks adhered to a power law, and organization networks to a power law with exponential cutoff. Censoring networks to exclude edges with less than 11 shared patients, a common de-identification practice for healthcare network data, markedly reduced edge numbers and greatly altered measures of vertex prominence such as the betweenness centrality. We identified patterns in the distance patients travel between network providers, and most strikingly between providers in the Northeast United States and Florida. We conclude that the choice of network construction algorithm is critical for healthcare network analysis, and discuss the implications for selecting the algorithm best suited to the type of analysis to be performed.