### Abstract

This paper gives an introductory overview of the concept of both random walks and electrical networks in graph theory using only undergraduate level mathematics. Random walks are stochastic processes that describe paths consisting of series of random steps in mathematical spaces. Electrical networks are intuitively interconnections of electrical components such as resistors, capacitors, and inductors in a circuit, modeled using current, voltage, and resistance; although in this paper we focus on electrical networks in the context of random walks. This paper covers fundamental definitions, history, rudimentary examples, and important theorems in both random walks and electrical networks and analyze the relationship between them.

Publication

MATH 4710 Graph Theory @ Vanderbilt University (Fall 2021)

###### Software Engineer

My interests include computer systems security and applied cryptography.