Social Network Analysis

Discrete Math · Axiom Academy

REAL WORLD Social Network Analysis Explore how graph theory reveals hidden patterns in social networks, from identifying influencers to discovering communities in real anonymized social media data. The Hidden Mathematics of Social Networks Every day, billions of people interact on social media platforms. But beneath the surface of likes, shares, and comments lies a fascinating mathematical structure called a graph . What is a Graph in Discrete Math? Nodes (Vertices): Represent individuals in the network Edges: Represent connections or relationships between people Properties: These graphs can reveal who's influential, how tight-knit groups are, and who belongs to which communities In this module, you'll analyze a real anonymized social network using three key graph metrics: clustering coefficient , centrality , and community detection . Below is a social network with 15 anonymized users. Each circle represents a person, and lines show connections (friendships or follows). Let's examine the structure! Notice: Some users have many connections (central nodes), while others have few. Some groups are tightly connected, while others are loosely linked. These patterns reveal important social dynamics! Metric 1: Clustering Coefficient The clustering coefficient measures how likely your friends are to be friends with each other. It captures the "cliquishness" of a network. C = (Number of triangles × 3) / Number of connected triples

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