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Using a dynamical model of happiness in humans, proposed in, we develop a model of happiness for a network of people using dynamical elements with interconnecting coupling factors. The network model of happiness is derived from a leader-followers network model proposed by Wang and Slotine. Such networks with interconnected dynamical elements can be found in sensor networks, electro-mechanical and biological systems. We consider the network of people as a dynamic leader-followers network and develop a new neural net-based observer for the dynamic network. The network observer approximates both the unknown dynamics of the nodes (human emotions) and the network coupling factors. The observer is used in propagation analysis of a fault in emotions. We introduce an emotional fault at the power-leader and study its detection at the leader and followers. To verify and validate the approach, we simulate the individual nodes, the network, and the network observer using Simulink that allows for intuitive and visual networking of dynamical elements.