Angiogenesis is an important process in the formation and maintenance of tissues which is driven by a complex system of intracellular and intercellular signaling mechanisms. Endothelial cells taking part in early angiogenesis must select their phenotype as either a tip cells (leading, migratory) or a stalk cells (following). Recent experiments have demonstrated that rapid calcium oscillations within active cells characterize this phenotype selection process and that these oscillations play a necessary role in governing phenotype selection and eventual vessel architecture. In this work, we develop a mathematical model capable of describing these oscillations and their role in phenotype selection then use it to improve our understanding of the biological mechanisms at play. We developed a model based on two previously published and experimentally validated mathematical models of calcium and angiogenesis then use our resulting model to simulate various multi-cell scenarios. We are able to capture essential calcium oscillation dynamics and intercellular communication between neighboring cells. The results of our model show that although the late DLL4 (a transmembrane protein that activates Notch pathway) levels of a cell are connected with its initial IP3 (Inositol 1,4,5-trisphosphate) level, cell-to-cell communication determines its eventual phenotype.