Capstone Literature Review 2

Capstone Literature Review 2 – Fall 2024

Dre Dyson

September 8, 2024

Table of Contents
1. Motivation and Introduction: 3
2. Methods Used: 3
3. Significance of the Work: 3
4. Connection to Other Work: 3
5. Relevance to Capstone Project: 4

1. Motivation and Introduction:
This article allows me to bridge my knowledge gap of various network types. While I had the opportunity to take a Complex Networks course at the University of West Florida, it provided a great introduction but only scratched the surface of Network Sciences. During the course, we covered foundational topics in graph theory and their application in the real world, such as social networks, biology, and how information spreads. Here we used several algorithms to build and analyze networks and find underlying patterns.
I enjoyed this course because we had the flexibility to choose a specific type of network to explore. However, this course was limited in the variety of networks we could explore in depth. Whereas, this article explores various network types, their applications, and the broader intricacies of Network Sciences. In a more general sense, the authors of this article wanted to apply knowledge of social networks to other domains, such as Epidemiology, information retrieval, and network resilience.

2. Methods Used:
The authors start by introducing the foundational graph theory problem, which is the Konigsberg Bridge problem. Here a mathematician, Carl Gottlieb Ehler, wondered if the city of Konigsberg, which has 7 bridges connecting two islands and two riverbanks, could be navigated such that a person could cross each bridge only once. This puzzle was eventually solved by mathematician Leonhard Euler, who stated this challenge was impossible. This justification was later known as the Eulerian path, which became a pivotable starting point in graph theory. The authors then expanded their knowledge of graph theory in social networks into several research questions to understand the following:
Characterize the structure and behavior of networked systems and suggest appropriate ways to measure these properties.
Create models of networks that help us understand the meaning of these properties.
In R1, the authors expand the definition of several network sciences metrics to establish many networks across various domains following the expected network properties. For example, the authors find most real-world networks follow a power-law distribution, meaning many nodes have a small number of edges, whereas a small number of nodes have many edges. Other metrics include the average path lengths that illustrate many real-world networks follow a small-worlds network, meaning the average path length is no more than six.

In R2, the authors expand several established models in network sciences to demonstrate that network behavior often has similar patterns across different domains. For example, they explore a community structure model to illustrate that many networks are organically organized into dense, distinct groups, with each group being sparsely connected to others. The authors then extend their analysis to include small-world and scale-free networks to show how these properties can predict network behavior, regardless of domain.

3. Significance of the Work:
Here the authors find many networks have a highly distinctive statistical signature of common networks of a wide variety of types. For example, many networks include high clustering coefficients and highly skewed degree distribution, which illustrates these networks oftentimes have hubs or authoritative figures. These findings suggest there are universal patterns underlying network structures.
4. Connection to Other Work:
Most of this study was built from previous work. Here the authors use foundational theories and models to develop their analysis. They build on established theories, such as Eulerian paths, Small-World networks, and power-law distributions to illustrate many networks behave the same, regardless of domain. By using previous studies, the authors provide network sciences that can be systemically applied to various domains.
5. Relevance to Capstone Project:
This article essentially lays the foundation for our project. First, it establishes that network science principles can be applied to a wide range of domains beyond traditional applications. Second, this article explains how our network should behave based on specific structural characteristics. Ultimately, we will use this article as a backbone to validate our findings and draw accurate conclusions.