#### Event Title

Modeling Social Networks with Random and Fuzzy Graphs

#### Presentation Type

Poster/Portfolio

#### Presenter Major(s)

Statistics, Mathematics

#### Mentor Information

Jiyeon Suh

#### Department

Mathematics

#### Location

Henry Hall Atrium 40

#### Start Date

11-4-2012 9:00 AM

#### Abstract

In this project, random weight graph models are extended to the fuzzy case, where fuzzy probability theory drives the stochastic process. To illustrate, suppose that an edge in a weighted graph is known to exist between two particular vertices but the strength of that edge is unclear. To determine the strength of this edge, we find the conditional expectation of a fuzzy random variable conditioned on the strength of mutual friends shared by the two vertices. The calculation of expected weight in this manner drives the stochastic process as a new vertex is connected randomly to the graph with each iteration. We discuss the efficacy of our approach as a modeling tool, interesting growth characteristics of the model, and possible modifications to the process.

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Modeling Social Networks with Random and Fuzzy Graphs

Henry Hall Atrium 40

In this project, random weight graph models are extended to the fuzzy case, where fuzzy probability theory drives the stochastic process. To illustrate, suppose that an edge in a weighted graph is known to exist between two particular vertices but the strength of that edge is unclear. To determine the strength of this edge, we find the conditional expectation of a fuzzy random variable conditioned on the strength of mutual friends shared by the two vertices. The calculation of expected weight in this manner drives the stochastic process as a new vertex is connected randomly to the graph with each iteration. We discuss the efficacy of our approach as a modeling tool, interesting growth characteristics of the model, and possible modifications to the process.