Calculating and Visualizing Network Metrics
2.2.1 Introduction
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Purpose: Network metrics (quantitative measures) complement visualization by helping analysts identify important vertices, subgroups, and the overall interconnectedness of a network.
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Aggregate Metrics: Used to compare entire communities (e.g., density).
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Individual Metrics: Used to identify specific actors’ roles, such as “popular” nodes or “bridge spanners.”
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NodeXL Integration: Metrics calculated in NodeXL can be mapped to visual properties (size, color, etc.) or used for filtering.
2.2.2 - 2.2.3 Computing Graph Metrics (The Kite Network)
The Kite Network (by David Krackhardt) is a standard example used to demonstrate different centrality measures.
2.2.3.1 Vertex-Specific Metrics
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Degree (Degree Centrality):
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A count of unique edges connected to a vertex.
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In-Degree (Directed only): Number of edges pointing to the vertex (e.g., being invited).
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Out-Degree (Directed only): Number of edges pointing away from the vertex (e.g., inviting others).
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Kite Example: Diane has the highest degree (6), making her the most “popular.”
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Betweenness Centrality:
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Measures how often a vertex lies on the shortest path (geodesic) between other vertices.
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Identifies “gatekeepers” or “brokers.”
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Kite Example: Heather has high betweenness because she is the only bridge between Ike/Jane and the rest of the group.
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Closeness Centrality:
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Measures the average shortest distance from a vertex to all others.
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Note: In NodeXL v1.0.1.113, a lower score meant more central. In newer versions, the inverse is used (higher is better).
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Kite Example: Fernando and Garth are best positioned to spread information quickly.
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Eigenvector Centrality:
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Calculates importance based on the importance of your neighbors. A link to a popular person is worth more than a link to a loner.
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Kite Example: Ed has a higher score than Heather because Ed is connected to the highly popular Diane.
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2.2. Clustering Coefficient:
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Measures how connected a vertex’s neighbors are to each other.
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A score of 1 means all your friends know each other (a clique).
2.2.3.3 Overall Graph Metrics (Summary Statistics)
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Connected Components: Groups of vertices connected to each other but separate from the rest.
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Diameter (Max Geodesic Distance): The longest “shortest path” between any two nodes in the network.
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Graph Density: A ratio (0 to 1) of actual edges to the total possible edges. Higher density = more interconnected.
2.2.4 Les Misérables Case Study (Weighted Networks)
This network connects characters from the novel based on co-appearance in scenes.
2.2.4.1 Weighted Edges
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Edge Weight: Represents the frequency of interaction (e.g., Valjean and Cosette appear in 31 scenes).
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Visualization: Edge weights are typically mapped to Edge Width or Edge Opacity. Using a Logarithmic Mapping is often better than linear for data with high variance.
2.2.4.3 Identifying Key Roles
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Jean Valjean: Highest Degree and Betweenness (the protagonist and main broker).
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Gavroche: Highest Eigenvector Centrality (the “courier” linking many different character groups).
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Myriel (The Priest): Low Degree but high Betweenness (he is the only link to several characters at the start of the book).
2.2.4.4 Metrics as Coordinates (Scatterplots)
NodeXL allows mapping metrics to X and Y coordinates rather than using a standard layout algorithm.
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Example: Degree on the X-axis and Betweenness on the Y-axis.
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Benefit: Makes outliers and “boundary spanners” (low degree but high betweenness) visually obvious.
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Graph Elements: You can display Axes and a Legend via the NodeXL ribbon under “Graph Elements.”
2.2.5 - 2.2.6 Summary and Research
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Practitioners: Combining quantitative metrics with visual attributes (like size/opacity) allows for a much deeper understanding of social roles than visualization alone.
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Researchers: Focus is currently on Parallelization (speeding up calculations for massive networks) and developing better metrics for Bipartite (multimodal) graphs.
Study Tip: Remember that Betweenness is about control/brokering (Heather in the Kite), while Closeness is about speed/access (Fernando/Garth).