Publication Date

5-2025

Date of Final Oral Examination (Defense)

3-7-2025

Type of Culminating Activity

Dissertation

Degree Title

Doctor of Philosophy in Computing

Department

Computer Science

Supervisory Committee Chair

Tim Andersen, Ph.D.

Supervisory Committee Member

Francesca Spezzano, Ph.D.

Supervisory Committee Member

Casey Kennington, Ph.D.

Abstract

The degree distribution of a real world network --- the number of links per node --- often follows a power law, so some hubs have many more links than traditional graph generation methods predict. For years, preferential attachment and growth have been the proposed mechanisms leading to these scale free networks, exemplified by the Barabási–Albert model. This dissertation provides an alternative model using a randomly stopped linking process, showing that mixtures of geometric distributions can lead to power laws, an intuition suggested by the Central Limit Theorem for distributions with infinite variance. Having a collection of Bernoulli trials with high variance is the commonality between the Barabási–Albert model and our Randomly Stopped Linking Model, implying that the critical characteristic of scale free networks is high variance. The limitation of classical random graph models is low variance in parameters, while scale free networks are the natural result of real world variance, with preferential attachment and growth being only one example mechanism.

DOI

10.18122/td.2411.boisestate

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