The document discusses different types of properties in network analysis including relational properties that measure relationships between nodes, and non-relational properties that measure attributes of individual nodes. It describes partition properties which assign discrete categorical labels to nodes, and vector properties which assign continuous numeric values. Methods for reducing large networks through partitioning are presented, such as extracting subnetworks of nodes with the same partition value or zooming in/out based on partitions. Temporal analysis of changes in node partition values over time is also mentioned.

2. PROPERTY
• Relational: Measure of Relations between 2 Nodes
• Line Value
• Non-Relational: Measure of Relation’s Parties
• Vertex Value: Color, Size, …
SVG Export

3. NON-RELATIONAL PROPERTY
• Discrete
Domain
• Continuous Number
Vector Partition
Structura
l
Attribute
• Statistical & Known Beforehand • Study of Network
• Structural Vector: Coordination of Vertex in an
Image
• Structural Partition: Central or Joining Vertex
• Partition Attribute: Poor or Wealthy Vertex
• Vector Attribute: ?

4. PARTITION PROPERTY
SMALL Discrete Value Domain Set
 Tries to partition the vertices into classes of same value
 Examples
 Gender = {Male, Female}; Partition Attribute
 Density = {Low, High, Huge}; Structural Partition
Partition values for each vertex is stored in separate *.clu file. The values can be edited.
By selecting a partition, it can drawn by Draw > Network + First Partition

5. VECTOR PROPERTY
Continuous Infinite Value Domain Set
• Example
• Coordination of Vertices in 2D (x, y) in R2 ; Structural Vector
• In case Vertices Represent Human  Height, Weight, .. ; Vector Attribute
• Partition  Vector
• Just Proper Meaning is Needed
• Vector  Partition
• Categorization of Values;
• Less, Between, Greater; e.g. Height  Tall, Medium, Short
• Truncate the Absolute Value
Vector values for each vertex is stored in separate *.vec file. The values can be edited.
By selecting a vector, it can drawn by Draw > Network + First Vector

6. VECTOR & PARTITION

7. REDUCTION  SUBNETWORK
In Case the Network is Very Large or Complex, Concentrate in Portion or
Generalize all of it …
Partition Property is the Main Tool
• Local View (Zoom In): Just Vertices of Same Partition Value
• Global View (Zoom Out): Treat Vertices of Same Partition Value as ONE
Vertex
• Contextual View: One Group to Zoom IN the Others to Zoom Out
• Exceptional Global View

8. Local View of North American Countries
Contextual View of Asian
Countries toward Other Continents
Global View of Countries as Continents

9. SUBNETWORK
• Extract Second Partition from First in Local View
• The Subnetwork Looses its Connection to the Original Network Partitions!
• Solution
1. Network has Two Partition P1 & P2
2. Extract Subnetwork for Value X of Partition P1
3. Want to Know P2 Values for the Subnetwork
4. Extract P1 for the Value X from P2  New Partition is Created
• Extract Subvector in Local View
• Accompany Local View based on a Partition with Vector
• Shrink Vector in Global View
• Accompany Global View based on a Partition with Vector
• For Each Partition of Same Value for Vertices Which Vector Value is
Chosen?
• Min, Max, Mean, …

10. TEMPORAL ANALYSIS
A Vertex may Change its Value of a Partition Value Migration to another
Value
• Statistical Analysis of the Change
• Cross-Tab
• Associativity
• Needs Two Partition File for the Same Partition Property for Different Time

11. QUESTION
• Reduction by Vector  Extract Subnetwork by Vector Values
• Solution: