Passive network reconstruction is the process of learning a structured (networked) representation of a dynamic system through the use of known information about the structure of the system as well as data collected by observing the inputs into a system along with the resultant outputs. This work demonstrates an improvement on an existing network reconstruction algorithm so that the algorithm is capable of consistently and perfectly reconstructing a network when system inputs and outputs are measured without error. This work then extends the improved network reconstruction algorithm so that it functions even in the presence of noise as well as the situation where inputs into the system are unknown. Furthermore, this work demonstrates the capability of the new extended algorithms by reconstructing financial networks from stock market data, and then performing an analysis to understand the vulnerabilities of the reconstructed network to destabilization through localized attacks. The creation of these improved and extended algorithms has opened many theoretical questions, paving the way for future research into network reconstruction.

Dynamical structure functions were developed as a partial structure representation of linear time-invariant systems to be used in the reconstruction of biological networks. Dynamical structure functions contain more information about structure than a system's transfer function, while requiring less a priori information for reconstruction than the complete computational structure associated with the state space realization. Early sufficient conditions for network reconstruction with dynamical structure functions severely restricted the possible applications of the reconstruction process to networks where each input independently controls a measured state. The first contribution of this thesis is to extend the previously established sufficient conditions to incorporate both necessary and sufficient conditions for reconstruction. These new conditions allow for the reconstruction of a larger number of networks, even networks where independent control of measured states is not possible. The second contribution of this thesis is to extend the robust reconstruction algorithm to all reconstructible networks. This extension is important because it allows for the reconstruction of networks from real data, where noise is present in the measurements of the system. The third contribution of this thesis is a Matlab toolbox that implements the robust reconstruction algorithm discussed above. The Matlab toolbox takes in input-output data from simulations or real-life perturbation experiments and returns the proposed Boolean structure of the network. The final contribution of this thesis is to increase the applicability of dynamical structure functions to more than just biological networks by applying our reconstruction method to wireless communication networks. The reconstruction of wireless networks produces a dynamic interference map that can be used to improve network performance or interpret changes of link rates in terms of changes in network structure, enabling novel anomaly detection and security schemes.