  Internet of Things(IoT) is a heterogeneous network consists of various
physical objects such as large number of sensors, actuators, RFID tags, smart
devices, and servers connected to the internet. IoT networks have potential
applications in healthcare, transportation, smart home, and automotive
industries. To realize the IoT applications, all these devices need to be
dynamically cooperated and utilize their resources effectively in a distributed
fashion. Consensus algorithms have attracted much research attention in recent
years due to their simple execution, robustness to topology changes, and
distributed philosophy. These algorithms are extensively utilized for
synchronization, resource allocation, and security in IoT networks. Performance
of the distributed consensus algorithms can be effectively quantified by the
Convergence Time, Network Coherence, Maximum Communication Time-Delay. In this
work, we model the IoT network as a q-triangular r-regular ring network as
q-triangular topologies exhibit both small-world and scale-free features.
Scale-free and small-world topologies widely applied for modelling IoT as these
topologies are effectively resilient to random attacks. In this paper, we
derive explicit expressions for all eigenvalues of Laplacian matrix for
q-triangular r-regular networks. We then apply the obtained eigenvalues to
determine the convergence time, network coherence, and maximum communication
timedelay. Our analytical results indicate that the effects of noise and
communication delay on the consensus process are negligible for q-triangular
r-regular networks. We argue that q-triangulation operation is responsible for
the strong robustness with respect to noise and communication time-delay in the
proposed network topologies.
