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\begin{acknowledgements} 
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There are many people without whom this dissertation would never have been completed.  Foremost among them is my advisor, Dr. {\bf Michele Benzi}.  Throughout this process, you were a constant source of help and guidance.  You have worked not only to help me complete my dissertation, but also to help establish me as a young researcher in the applied mathematics community and for this I am extremely grateful.

I would also like to thank my committee members, Dr. {\bf Ronald Gould} and Dr. {\bf James Nagy}.  I truly appreciate the time and energy you have taken to help make my thesis the best possible.

Throughout the past five years, the Emory Mathematics and Computer Science Department has been my home base.  I would like to thank all the faculty, staff, and other graduate students for making the department what it was.

Additionally, I would like to thank Prof. {\bf Ernesto Estrada} (University of Strathclyde) for providing research ideas and datasets used throughout this thesis.   

I would be remiss not thank to Mr.~{\bf Yu Wang} (Emory University)
for performing the calculations with the Wikipedia graph in Chapter \ref{C:TotalComm}, and Dr. {\bf Tamara Kolda} (Sandia National Laboratories) and Dr. {\bf David Gleich} (Purdue University) for providing valuable suggestions for the work in Chapter \ref{C:HubsAuths}.

In addition, I wish to thank Dr. {\bf Tamara Kolda} and Dr. {\bf Blair Sullivan} (NC State University) for providing me with opportunities to work at, respectively, Sandia and Oak Ridge National Labs during my summers.  These internships have helped me grow as a researcher and introduced me to exciting new projects.

Finally, I would like to express my deepest gratitude to all my friends and family who supported me throughout this process.  A special thanks goes out to my parents, Drs. {\bf Paul and Nancy Klymko}.  You both gave me more support than anyone has a right to expect. 

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