Harsh RB

SNA 1.3

4 min read

Study Notes: Social Network Analysis (Chapter 3)

1.3.1 Introduction to Networks

  • Definition: A network is a collection of things and their relationships to one another.

  • Components:

    • Vertices (Nodes): The “things” connected (people, items, institutions).

    • Edges (Ties/Links): The connections between the vertices.

  • Purpose: Visualize complex relationships as maps (sociograms) and calculate precise measures of size, shape, and density.

1.3.2 The Network Perspective

  • Relational vs. Attribute Data: Traditional social science focuses on individual attributes (age, gender). Network science focuses on the connective tissue—the relationships between individuals.

  • Location, Location, Location: An individual’s success is often determined by their position within a structure rather than internal abilities alone.

  • Social Metrics: Recognizes patterns like “popularity” (many connections) vs. “influence” (connections to other well-connected people).

1.3.2.1 A Simple Twitter Network Example

  • Sociogram: A visual network graph.

  • Visual Overlay: Attribute data (like total tweet count) can be used to determine the size of a vertex in the graph.

1.3.2.2 Vertices and Edges

  • Vertex Attributes: Demographic data (race, age) or system data (logins, posts) can be mapped to visual properties like color or size.

  • Edge Types:

    • Directed (Asymmetric): Clear origin and destination (e.g., following someone on Twitter, sending an email). Represented by arrows.

    • Undirected (Symmetric): Mutual relationship with no direction (e.g., being Facebook friends, being married).

    • Unweighted (Binary): Simply shows if a tie exists (1) or not (0).

    • Weighted: Shows the strength or frequency of the tie (e.g., number of messages exchanged).

1.3.2.4 Data Representations

  • Adjacency Matrix: A table where rows and columns both represent individuals.

  • Edge List: A two-column list identifying pairs of connected vertices (Vertex 1 Vertex 2). This is the preferred format for NodeXL.

1.3.3 Types of Networks

  • Egocentric Networks: Focused on a single individual (Ego) and their connections (Alters).

    • 1-degree: Ego + Alters.

    • 1.5-degree: Ego + Alters + connections between those Alters.

    • 2-degree: Ego + Alters + Alters’ friends.

  • Full vs. Partial: A full network includes everyone in a system; a partial network is a “slice” (e.g., users of a specific hashtag).

  • Unimodal vs. Multimodal:

    • Unimodal: One type of vertex (e.g., person-to-person).

    • Multimodal (Bimodal/Affiliation): Two or more types (e.g., people connected to the documents they edit).

  • Multiplex: Networks with multiple types of edges between the same vertices (e.g., two people who are both “coworkers” and “friends”).

1.3.4 & 1.3.5 Network Analysis Metrics

1.3.5.1 Aggregate Metrics (Whole Network)

  • Density: The percentage of all possible connections that actually exist. Measures cohesion.

  • Centralization: Measures how much the network revolves around a few key nodes.

1.3.5.2 Vertex-Specific Metrics (Individual Positions)

  1. Degree Centrality: Simple count of total connections.

    • In-degree: Connections pointing to the vertex (popularity).

    • Out-degree: Connections pointing away (sociability).

  2. Betweenness Centrality: Measures how often a vertex acts as a bridge on the shortest path between others. High scores indicate a broker role.

    • Structural Hole: A gap between two groups; the person who fills this gap has high strategic value.

1.3. Closeness Centrality: The average distance (number of hops) from a vertex to all others. Low scores mean you are “close” to everyone.

  1. Eigenvector Centrality: Influence score. You are central if you are connected to other highly central people (e.g., Google’s PageRank).

  2. Clustering Coefficient: Measures the density of an individual’s 1.5-degree network (do your friends know each other?).

1.3.6 - 1.3.9 Historical and Technical Context

  • Small World Phenomenon: “Six Degrees of Separation”—most nodes can be reached in a small number of steps.

  • Weak Ties: Mark Granovetter’s theory that “weak ties” (acquaintances) are more useful for finding new information/jobs than “strong ties” (close friends).

  • Dunbar’s Number: The theoretical biological limit of ~150 stable social relationships.

  • Netviz Nirvana: The ideal state of a visualization where every vertex/edge is visible, clusters are identifiable, and outliers are clear.

1.3.10 Common Exam/Research Questions

  • Social Roles: Who is the “Answer Person” or the “Boundary Spanner”?

  • Influencers: Who helps new ideas propagate?

  • Community Health: How do structures change after events like layoffs or mergers?

Study Tip: Focus on the difference between Betweenness (brokering/bridging) and Eigenvector (influence by association). These are common points of confusion in SNA exams.

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