It is common for people to access multiple social networks, for example, using phone, email, and social media. Together, the multi-layer social interactions form a "integrated social network." How can we extend well developed knowledge about single-layer networks, including vertex centrality and community structure, to such heterogeneous structures? In this paper, we approach these challenges by proposing a principled framework of network composition based on a unified dynamical process. Mathematically, we consider the following abstract problem: Given multi-layer network data and additional parameters for intra and inter-layer dynamics, construct a (single) weighted network that best integrates the joint process. We use transformations of dynamics to unify heterogeneous layers under a common dynamics. For inter-layer compositions, we will consider several cases as the inter-layer dynamics plays different roles in various social or technological networks. Empirically, we provide examples to highlight the usefulness of this framework for network analysis and network design.