Network Science

4Network Optimization

4.1 Introduction

The mathematical science behind network analysis and network optimization is the graph theory. Several concepts and centrality measures associated with network analysis and network optimization come from graph theory. One of the greatest advantages of graph theory is the mathematical formulation, the formalism that allows us to develop algorithms to be run on computers in order to solve business problems.

Graphs are considered mathematical structures used to model pairs of relations between objects or entities. The study of graphs considers a set of nodes or vertices (the entities or objectives mentioned before), and a set of links or edges (the relations between those objects or entities). The links are used to represent all the connections between the nodes in the graph. These connections are associated with a pair of nodes. These pairs of nodes can be represented by distinct nodes, or by a single node. A connection based on a single node usually refers to an auto‐relationship, which a node connects to itself. For example, if an author refers to a paper they published before, that author refers to themself in an authorship graph. Analogously to social science, when we seek descriptions about people's relationships, the graph theory provides explanations about entities and relations. However, as opposed to social sciences, graph theory uses mathematical formalism to describe these relations. Based on mathematical formulas to describe ...