Using Network Reliability to Understand International Food Trade Dynamics.

Understanding the structural and dynamical properties of food networks is critical for food security and social welfare. Here, we analyze international trade networks corresponding to four solanaceous crops obtained using the Food and Agricultural Organization trade database using Moore-Shannon network reliability. We present a novel approach to identify important dynamics-induced clusters of highly-connected nodes in a directed weighted network.

Determining whether a class of random graphs is consistent with an observed contact network.

We demonstrate a general method to analyze the sensitivity of attack rate in a network model of infectious disease epidemiology to the structure of the network. We use Moore and Shannon's "network reliability" statistic to measure the epidemic potential of a network. A number of networks are generated using exponential random graph models based on the properties of the contact network structure of one of the Add Health surveys.

From network reliability to the Ising model: A parallel scheme for estimating the joint density of states.

Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a reliability property, Ising feasibility, for which the network reliability is the Ising model's partition function. As shown by Moore and Shannon, the network reliability can be separated into two factors: structural, solely determined by the network topology, and dynamical, determined by the underlying dynamics.