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We propose a simple but effective algorithm to formulate growable communication graphs that exhibit (i) fast information dissemination, (ii) high scalability with negligible performance degradation, and (iii) very small diameter and short average path length. In particular, we use Borel Cayley Graphs (BCGs) as base network topologies. Previously, we reported that BCGs are one of the fastest information dissemination topologies. However, practical applications of BCGs to real networks have been challenging because of its lack of size flexibility. The proposed BCG Random Expansion algorithm resolves such size restrictions. Simulation results revealed that the proposed algorithm successfully expands the original BCGs. In fact, even after 25 times of expansion, the expanded BCGs display almost the same or superior topological properties as the original BCGs, such as a small diameter and a short average path length. In the last part of this paper, we discuss the information dissemination performance of communications graphs. Simulation results confirmed that the information dissemination performance of the expanded BCGs remains very close to that of the original BCGs regardless of the amount of expansion.