Two-mode networks

Kaibin He

Outline

• Data structure• Visualization• Quantitative Analysis• Qualitative Analysis

Rectangular data array

1 2 3

A 0 1 0

B 1 0 1

1 2 3

A 0 1 0

B 1 2 1

Two-mode to One-mode• Data>Affiliations

• Cross-product(binary data) : multiplies each of A's scores by the corresponding score for B, and then sums across the columns

1 2 3

A 0 1 0

B 1 0 1

1 2 31 1 0 1

2 0 1 0

3 1 0 1

A B

1 0 1

2 1 0

3 0 1

Two-mode to One-mode

• Minimums (valued data): examines the entries of A and B for campaign 1, and selects the lowest score (zero). It then does this for the other campaigns and sums.

1 2 31 1 1 1

2 1 3 1

3 1 1 1

1 2 3

A 0 1 0

B 1 2 1

A B

1 0 1

2 1 2

3 0 1

Bipartite

• The matrix is formed by adding the rows as additional columns, and columns as additional rows. Transform>Bipartite

1 2 3

A 0 1 0

B 1 0 1

A B 1 2 3

A 0 0 0 1 0

B 0 0 1 0 1

1 0 0 0 0 0

2 0 0 0 0 0

3 0 0 0 0 0

Visualization

• Netdraw>File>UCINET dataset>2-Mode Network

• Use scaling method to locate the points

• Example: Zhou, Yuan, Wang (2013)

Quantitative analysis

• Identify underlying dimensions of the joint space of actor-by-event.

• Two-mode SVD analysis. (valued data)Tools>Scaling/Decomposition>SVD

• Two-mode factor analysis. (valued data)Tools>Scaling/Decomposition>Factor Analysis

• Two-mode correspondence analysis. (binary data)Tools>Scaling/Decomposition>Correspondence

SVD

• Singular Values• RCScores• Row Scores• Column Scores• Scatter Plot

• Example

Factor Analysis

• Eigenvalues• Loadings• Scatter plot

• Example

Correspondence analysis

• Row/Column Scores• Scatter plot

• Example

Qualitative analysis

• Block models

• Two-mode core-periphery analysis. Network>2-Mode>Categorical Core>Periphery

• Two-mode factions analysis Network>2-Mode>2-Mode Factions

Two-mode core-periphery analysis

• The "core" is a cluster of frequently co-occurring actors and events.

• The "periphery" consists of a partition of actors who are not co-incident to the same events.

• 0 means bad fit, 1 means excellent fit.• Ideal density matrix

1 2

1 1

2 0

Two-mode factions analysis

• Factions are groupings that have high density within the group, and low density of ties between groups.

• Example

Recommended paper

The Quest for Content: How User-GeneratedLinks Can Facilitate Online Exploration

JACOB GOLDENBERG, GAL OESTREICHER-SINGER, and SHACHAR REICHMAN JMR, 2012

• Is social network important to e-business?

product pages linked by hyperlinks & user generated links

conclusion

This dual-network structure in facilitating content exploration.