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Understanding the Hypercube

The hypercube is a powerful abstraction for analyzing data from multiple perspectives. Think of a simple cube with three dimensions: length, width, and height. A hypercube extends this concept to an arbitrary number of dimensions, allowing you to model complex business scenarios.

Each axis of the hypercube represents a key dimension of your data, such as:

  • Time (e.g., year, month, day)
  • Geography (e.g., region, country, city)
  • Product (e.g., category, brand, item)
  • Customer (e.g., segment, demographics)

The hypercube enables you to calculate metrics (like sales, revenue, or user counts) across any combination of these dimensions, ensuring your calculations are always consistent and reusable. For example, you can analyze:

  • Revenue by Month

  • Active users by Month and Product Category

  • Margin by Month, Product Category, and Region

Data Model as a Graph

This is how Cube Alchemy Builds an Hypercube. The underlying structure is a Connected Undirected Acyclic Graph where:

  • Nodes: Your DataFrames.
  • Edges: Shared columns link tables. **

It might not look like a tree, but under the hood, the hypercube is basically a tree in disguise — no loops, just clean branches connecting your data. See: Tree (graph theory).

  • Effortless Queries: The hypercube handles the relationships for you. When you request a metric across certain dimensions, the hypercube automatically traverses these connections to gather the necessary data.

  • Consistency: Define your metrics and queries once; they will be stateful and can be used reliably across the entire analysis journey.

Notes:

** Practically, when three or more tables share the same column name, linking them directly would create cycles. Cube Alchemy prevents this by:

  • creating an extra node (a link table) with the distinct shared values,

  • replacing the original column in each table with an auto‑numbered key,

  • keeping the original column name only in the link table,

  • using those key columns solely to connect tables (they’re internal and hidden for users).

Avoid Circular Dependencies

For the hypercube to function correctly, your data model must be a Acyclic Graph. This means you must avoid cyclic relationships (or circular references). Such cycles create ambiguous join paths that break the logic of data traversal and aggregations.

With proper modeling (e.g., bridge tables, role-playing/conformed dimensions, etc) cycles can be addressed. Trees keep results consistent and avoid the ad‑hoc rules general graphs require.