Lecture 01 : Network Data - Some Stories !!

Introduction

This tutorial provides an overview of key concepts related to network data analysis, particularly in the context of historical marriage alliances and financial institutions. By exploring the Florentine marriage network and the interconnectedness of banks, you'll gain insights into how data can reveal underlying power structures and relationships.

Step 1: Understanding Network Data

• Definition of a Network: A network consists of nodes (or vertices) and edges (connections between nodes). In our examples, nodes represent families or banks, while edges represent relationships or connections.
• Identifying Neighbors and Connections:
  • Nodes are called neighbors if there exists an edge between them.
  • Two nodes are connected if there is a path (not necessarily direct) between them.

Step 2: Exploring Historical Marriage Alliances

• Historical Context: Marriage alliances in 14th-15th century Florence were a strategy for political power. The Medici family is a prime example of this.
• Florentine Marriage Network:
  • Families are represented as nodes.
  • An edge between two families indicates a marriage.
• Analyzing Power Structures:
  • Use the network to infer power dynamics. The Medici family can often be identified as a key player based on their connections.

Step 3: Mathematical Concepts in Networks

• Betweenness Centrality:
  • This metric indicates the importance of a node based on its position in the network.
  • Calculate the betweenness centrality of a node K using the formula:

    Betweenness Centrality of K = (Number of times K appears in shortest paths between pairs of nodes) / (Total number of shortest paths)
    

• Calculating Betweenness:
  • Assess how many shortest paths exist between various pairs of nodes and how many of those paths pass through the node in question.

Step 4: Understanding Prestige in Networks

• Cat's Prestige:
  • This measure reflects the power of a node based on the prestige of its neighbors.
  • Calculate Cat's Prestige for a node I using:

    Cat's Prestige of I = Sum of (Prestige of each neighbor / Degree of that neighbor)
    

• Importance of Degree: The more connections a powerful neighbor has, the less prestige that power transfers to node I.

Step 5: Analyzing Financial Institutions' Interconnectedness

• Study of Banks: A network analysis of 96 major banks illustrates their interconnectedness.
• Volatility Measurement:
  • Define volatility using stock price observations:

    Volatility = f(Highest price, Lowest price, Closing price, Opening price)
    

• Directional Connectedness:
  • Calculate how the volatility of one bank influences another to understand systemic risk.

Step 6: Systemwide and Total Directional Connectedness

• Understanding Systemwide Connectedness:
  • This is the average total directional connectedness across all banks.
  • It highlights how interconnected the banks are within the financial system.

Conclusion

This tutorial outlined foundational concepts in network data analysis, illustrated through historical examples and financial institutions. Key takeaways include understanding network structure, applying mathematical metrics like betweenness centrality and Cat's Prestige, and analyzing the interconnectedness of financial entities. For further exploration, consider conducting your own network analysis using real-world data to uncover patterns and relationships.