A Proposition for Describing Real-World Network Dynamics
Authors: Yang Chun-Lin , Shettigar Nandan , Suh C. Steve 
Published: January 2022

Abstract
This study presents a proposition for describing the dynamics of real-world networks under the general framework of complex networks. Outward behaviors of complex networks are the manifestation of the coupled dynamics at the macroscopic level and the individual dynamics at the microscopic level. At the macroscopic level a law of coupling governs the interactions of network constituents. At the microscopic level, the dynamics of individual constituent is defined by energy that follows normal distribution. Constituent dynamics are bounded by physical constraints. Consequently, network dynamics can be quantified using information entropy which is a function of constituent energy. In real-world networks, differences between individual constituents exist due to differing mechanical properties and dynamics. Consequently, network dynamics are of different layers and hierarchies. Construct of network governing equations formulated under the general framework of complex networks are demonstrated using two real-world networks — a brain network and a lymph node network. Brain network is constructed by the neurons that each connected by the synapse. Brain network dynamics is composed by the law of coupling defined by the synaptic dynamics through the transmitting of neurotransmitters that couples the individual neuron dynamics. Since different classifications exist among neurotransmitters and neurons, the post synaptic neuron can present either inhibitory or excitatory action. The inhibitory and excitatory behavior of the neurons changes the mechanical properties of each neuron and further alters the brain network dynamics. Consequently, the brain network emerges dynamics with different layers. Lymph node network drains fluid from blood vessels, filter the lymph (the interstitial fluid lymphatic system collects from the blood circulation) through lymph nodes, and transport the lymph back to the blood circulation. Lymph node dynamics is composed by the dynamics of lymph transportation along the lymph node network and the individual lymph node dynamics that involves lymphocytes-pathogens interactions (adaptive immune response). In each lymph node, lymphocytes fight off the pathogens which also emerges a network dynamics such as the interaction between T cells and HIV viruses. Finally, the lymph is collected from each lymph nodes and drained back to the blood circulation. As a result, the lymph node network has the dynamics of different hierarchies where the lymphocytes-pathogens dynamics exists within each lymph node at the lower hierarchy is further under the influence of the lymph transportation dynamics among the whole lymph node network on the higher hierarchy. Since the constituent dynamics of the brain network and lymph node network can be defined by energy that follows normal distribution and both are bounded by physical constraints, the network dynamics of both cases can be quantified through information entropy. Features pertaining to the global as well as individual constituent dynamics of the networks are identified that are insightful to the control of such complex networks.