Blockchain allows to securely store, using cryptography functions, validated transactions and other data across its peer to peer (P2P) network. This P2P network is generated and maintained by the participating peers in a distributed manner through peer discovery, neighbor selection and managing inbound/outbound connections. As these tasks require extra consumption of network bandwidth, energy, memory and CPU usage, resource-limited devices may not support inherent blockchain applications. Further, changes in the topology control functions or reconfiguration should be considered by all peers to fully benefit from the new performance, which can take time. The aim of this paper is to build a blockchain network in a manner that greatly reduce topology control overhead while guaranteeing the properties such as high flexibility, fast reconfigurability, connectivity, small diameter and clustering. For this, we propose to use the Software-Defined Networking (SDN) paradigm to manage the blockchain P2P network. This way, the topology control tasks are moved off the peers to a secure overlay layer composed of multiple servers having synchronized databases. This new layer is responsible for building and managing the topological structure of the P2P network layer based on random rout digraphs. Next, we mathematically discuss rout digraphs generation using binomial distribution and preferential attachment models. Then, and in order to reduce the number of connections per peer, we establish lower and minimum upper bounds on outbound and inbound connections respectively that still guarantee the P2P network feasibility and connectivity. Further, we investigate topological properties of blockchain P2P network such as connectivity, diameter and clustering. Finally, we provide extensive simulation and numerical results to verify the efficiency of our approach and illustrate the effects of centralized topology control on network performance.