Mathematics for some classes of networks

TL;DR

This paper reviews various mathematically rigorous classes of networks and introduces a new class related to markets with many agents, highlighting the mathematical foundations for complex network analysis.

Contribution

It provides an overview of existing network classes and introduces a novel class linked to multi-agent market systems.

Findings

Overview of well-defined network classes

Introduction of a new network class related to markets

Mathematical foundations for complex networks

Abstract

Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of networks which interested the authors for some time. In section 4 we consider in detail a new class of networks, related to markets with many agents.