4.1 Fundamentals of Social Network Theory

Social networks are complex webs of connections between people or entities. Understanding their structure helps us analyze how information spreads and relationships form. This topic dives into the building blocks of networks and the math behind them.

We'll explore ways to measure importance in networks, like finding key influencers. We'll also look at different types of relationships and how they shape network structure. These concepts are crucial for understanding how social media platforms function and grow.

Network Components

Fundamental Elements of Networks

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• Nodes represent individual actors or entities within a network (people, organizations, websites)
• Edges connect nodes, indicating relationships or interactions between them
• Directed edges show one-way relationships (follower connections on Twitter)
• Undirected edges represent mutual or reciprocal relationships (Facebook friendships)
• Weight of edges can signify strength or frequency of connections

Graph Theory Foundations

• Graph theory provides mathematical framework for analyzing network structures
• Adjacency matrix represents network connections in tabular form
• Path length measures number of edges between two nodes
• Degree of a node indicates number of direct connections it has
• Clustering coefficient quantifies how tightly connected a node's neighbors are
• Network density calculates proportion of possible connections that actually exist

Centrality Measures

Types of Centrality

• Centrality identifies most important or influential nodes in a network
• Degree centrality measures number of direct connections a node has
• Eigenvector centrality considers importance of a node's connections
• Katz centrality extends eigenvector centrality to handle directed networks
• PageRank algorithm uses similar principles to rank web pages

Betweenness and Closeness

• Betweenness centrality quantifies how often a node acts as a bridge between others
• Nodes with high betweenness often control information flow in networks
• Closeness centrality measures how quickly a node can reach all others in network
• Harmonic centrality offers alternative to closeness for disconnected networks
• Centrality measures help identify key influencers, gatekeepers, and vulnerable points

Social Network Concepts

Relationship Dynamics

• Social ties form connections between individuals or groups in a network
• Strong ties represent close relationships (family, close friends)
• Weak ties often provide access to diverse information and opportunities
• Homophily describes tendency of similar individuals to connect (shared interests, demographics)
• Triadic closure predicts formation of new connections among mutual acquaintances

Network Structures and Phenomena

• Structural holes refer to gaps between disconnected groups in a network
• Individuals bridging structural holes often gain information and control advantages
• Small world phenomenon describes short average path lengths in large networks
• Six degrees of separation concept stems from small world studies
• Scale-free networks feature few highly connected nodes and many less connected ones
• Preferential attachment explains growth of scale-free networks (popular nodes attract more connections)