The growing dominance of encrypted network traffic and modern encryption protocols (TLS 1.3, QUIC, DoH) poses significant challenges for accurate network classification, particularly as many existing approaches rely on text- or image-based representations, which fail to adequately capture the inherent structural relationships present in network communication-relationships that are more naturally represented as graphs. In this work, we introduce GraphMux, a graph-based framework that leverages line graph transformations to fuse multiple graph views into a unified representation. We also present three graph-based flow representations (TIG+Chain, StarBurst, and 2Chain) designed to capture both temporal burst dynamics and client-server interaction patterns, using only packet time, direction, and length information, without incorporating any unencrypted statistical features. We evaluate our approach on three datasets: two academic datasets (UTMobileNetTraffic2021 and QUIC PCAP) and a commercial dataset (Flash), using four graph embedding architectures. Across all datasets, GraphMux consistently achieves superior performance, and the proposed graph constructions often yield the best results. Additional experiments examining attribute-selection strategies reveal a strong positive relationship between well-aligned feature assignments and classification accuracy, underscoring the importance of principled attribute design when constructing graph representations for encrypted traffic.