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Synopsis

Differences or similarities in networks are typically discovered in a side-by-side comparison.

We can simplify this process by visualizing the differences or similarities between two hive plots as a differential hive plot.

Set Operations

Differential hive plots can be constructed by performing a set operation on two given hive plots "A" and "B":

OperationDenotationEffect
intersectionA ∩ BSelect similar nodes and edges from "A" and "B".
relative complementA ∖ BSelect nodes and edges from "A" that are not found in "B".
symmetric differenceA Δ BSelect unique nodes and edges from each plot.
unionA ∪ B

Select all nodes and edges from "A" and "B".

Equivalent to joining the results of intersection and symmetric difference.

Here are 4 different differential hive plots:

Definition of Similarness

Two edges are similar if all of the following are met:

  • sources are on the same axis
  • sinks are on the same axis
  • directionality must agree for directed edges only
  • positions of the sources are within the margin of error
  • positions of the sinks are within the margin of error
  • sources have the same name (optional)
  • sinks have the same name (optional)

Margin of Error

The margin of error defines the degree of similarness. There are 2 types of error:

TypeDefinition
Absolute Error

The difference in the original values used to define the node's position on the hive plot.

Domain: same as the parameter chosen for node position assignment

Relative Error

The difference in the node's relative position on the axis.

Domain: (0,1)

Attributes for Format Rules

Every node or edge in a differential hive plot is assigned a value for the src attribute:

ValueDefinition
AThis item is unique to hive plot "A".
BThis item is unique to hive plot "B".
ABThis item is common to both hive plots "A" and "B".

In the 4 examples above, format rules were applied to assign colors based on the src attribute.

Nodes that are not similar are assigned a value for the diff attribute:

ValueDefinition
onaxisNodes are on the same axis but no within the margin of error.
offaxisNodes are on different axis.
offplotThe node is not found in the other hive plot.
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