This thesis is concerned with multigraphs and their complexity which is defined and quantified by the distribution of edge multiplicities. Two random multigraph models are considered.  The first model is random stub matching (RSM) where the edges are formed by randomly coupling pairs of stubs according to a fixed stub multiplicity sequence. The second model is obtained by independent edge assignments (IEA) according to a common probability distribution over the edge sites. Two different methods for obtaining an approximate IEA model from an RSM model are also presented. In Paper I, multigraphs are analyzed with respect to structure and complexity by using entropy and joint information. The main results include formulae for numbers of graphs of different kinds and their complexity. The local and global structure of multigraphs under RSM are analyzed in Paper II. The distribution of multigraphs under RSM is shown to depend on a single complexity statistic. The distributions under RSM and IEA are used for calculations of moments and entropies, and for comparisons by information divergence. The main results include new formulae for local edge probabilities and probability approximation for simplicity of an RSM multigraph. In Paper III, statistical tests of a simple or composite IEA hypothesis are performed using goodness-of-fit measures. The results indicate that even for very small number of edges, the null distributions of the test statistics under IEA have distributions that are  well approximated by their asymptotic χ2-distributions. Paper IV contains the multigraph algorithms that are used for numerical calculations in Papers I-III.

Adopted in 2003, the National Incident Management System is the nation’s first standardized management system unifying the actions of all levels of governments during a large-scale emergency response. It sets the standard for interagency coordination and communication in the event of an emergency. This professional report seeks to produce a working, NIMS-compliant emergency communication plan for the City of Austin, Texas. The report begins with an explanation of NIMS, focusing on the national protocols for interagency communication and public information. It then presents a case study of emergency communications in practice, examining two firestorms in San Diego County, California that occurred four years apart – prior to and after the County’s implementation of NIMS communications protocols. The report synthesizes best practices in emergency communications – from both NIMS research and the San Diego case study – to create the City of Austin Public Information and Emergency Communication Plan, an operational guide that fully utilizes the tools and organizational structure of all City departments, including the City’s Communications and Public Information Office. / text

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