A Underwater acoustic sensor networks (UASNs) are the technology that enables various underwater applications, and the interest in UASNs is growing. UASNs consist of underwater sensors anchored nodes and surface sinks that perform collaborative monitoring tasks over a three-dimensional deployment space. A Complex Network Approach to Topology Control Problem in Underwater Acoustic Sensor Networks Anchored nodes are equipped with floating buoys inflated by pumps, and the depth of the anchored node is regulated by adjusting the length of the wire. The buoyant force from buoys is far greater than the gravity of nodes. As shown in the measurements of environmental events are locally A Complex Network Approach to Topology Control Problem in Underwater Acoustic Sensor Networks monitored by the anchored nodes, and transferred to a surface sink by multi-hops. Both electromagnetic waves and laser waves are not suitable for underwater transmission, and acoustic communication is the typical physical layer technology in UASNs. A Complex Network Approach to Topology Control Problem in Underwater Acoustic Sensor Networks Therefore, the distinguishing feature of UASNs is propagation delay because acoustic waves are much slower than electromagnetic waves the speed of acoustic waves is approximately 1500m/s. Consequently, propagation delay in UASNs cannot be neglected. A Complex Network Approach to Topology Control Problem in Underwater Acoustic Sensor Networks Another inevitable issue regarding UASNs is signal irregularity signal is not uniform in all directions, which is caused by various factors, such as antenna directions and gains, transmitting power, battery status, signal-tonoise ratio threshold, and obstacles . In particular, various obstacles are distributed in underwater environments: thus, signals are more easily reflected, diffracted, or scattered during propagation , A Complex Network Approach to Topology Control Problem in Underwater Acoustic Sensor Networks so probabilistic coverage and connectivity problems are more appropriate for acoustic detection applications. Signal irregularity directly or indirectly affects the performance of network protocols, such as the MAC, routing, localization and topology control. Therefore, signal irregularity is a non-negligible issue, especially in UASNs. Moreover, the battery power of nodes is limited. Batteries usually cannot be easily replaced underwater, and solar energy is rarely exploited as well.