Existing graph data management systems still provide limited support for evolving and temporal data. In addition, time-series data often reside outside graph engines, hindering unified analysis. HyGraph is a new hybrid approach to manage and analyze both temporal graph and time series data in a unified manner. In particular, it supports rich transformations between graph and time-series data. We discuss two novel operators on HyGraph to illustrate such transformations, a time-series-based graph operator and a graph-based time-series operator. The first ingests time-series data and produces a new graph (or a subgraph) that captures relationships among time series based on correlation values. The second operator, in contrast, generates a time series based on the evolution of temporal graph metrics, such as aggregated edges or changes in node degree. The transformation operators allow the augmentation of derived values to the hybrid structure for self-enrichment. We also outline open challenges of dynamic transformations within the hybrid model.