What question did this study set out to answer?

To explore the application of graph theory in analyzing gene networks and Markov chains.

May 16, 2026Open Access

Graphs, Markov Chains, and Gene Networks

Key Points

To explore the application of graph theory in analyzing gene networks and Markov chains.
Introduced definitions and theorems of graph theory.
Presented basic functionality of igraph, an R package.
Included an application to gene networks.
Outlined various applications of graph theory including neural networks and protein interactions.
Demonstrated the utility of igraph in modeling gene networks.

Abstract

Graph theory (also called network analysis) is employed in many fields of applied mathematics: in statistics, graphs can be used to describe and analyze many properties of Markovian chains and neural networks; in mechanics, they are employed to model kinematic chains, in biology the concept of protein-protein interaction finds an immediate translation into weighted graphs; in computer science, graph theory is among the theoretical bases of operations research. In this short document, I’ll present some definitions and theorems, and I will introduce the basic functionality of igraph, an R package. At the end of this document, I present an application of graph theory to the study of gene networks.

Graphs, Markov Chains, and Gene Networks

Key Points

Abstract

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