We incorporate underlay information into overlay design for topic-based publish/subscribe (pub/sub) systems on geo-distributed data centers. We propose the MinAvg-WTCO problem that optimizes the weighted average node degree while constructing a topic-connected overlay (TCO), i.e., Each topic induces a connected sub-overlay among all nodes interested in this topic. Most existing TCO designs are oblivious to the low-level network infrastructure and assume edge equivalence. We prove that MinAvg-WTCO is NP-complete and difficult to approximate within a logarithmic factor with regard to the number of nodes. We devise several approximation algorithms for MinAvg-WTCO using different design techniques. Both theoretical analysis and empirical evaluation show that our designed algorithms tread the balance between overlay quality and runtime cost. Our algorithms significantly outperform the state of the art for TCO design that ignores edge differences.