We present TikTok StitchGraph: a collection of 36 graphs based on TikTok stitches. With its rapid growth and widespread popularity, TikTok presents a compelling platform for study, yet given its video-first nature the network structure of the conversations that it hosts remains largely unexplored. Leveraging its recently released APIs, in combination with web scraping, we construct graphs detailing stitch relations from both a video- and user-centric perspective. Specifically, we focus on user multi-digraphs, with vertices representing users and edges representing directed stitch relations. From the user graphs, we characterize common communication patterns of the stitch using frequent subgraph mining, finding a preference for stars and star-like structures, an aversion towards cyclic structures, and directional disposition favoring in- and out-stars over mixed-direction structures. These structures are augmented with sentiment labels in the form of edge attributes. We then use these subgraphs for graph-level embeddings together with Graph2Vec, we show no clear distinction between topologies for different hashtag topic categories. Lastly, we compare our StitchGraphs to Twitter reply networks and show that a remakable similarity between the conversation networks on the two platforms.