How to read a DSM?¶

A DSM, or Dependency Structure Matrix, is a great way to display dependencies or interfaces between entities. A DSM is closely related to the adjacency matrix of a graph. A graph or network with nodes (entities) and edges (interfaces) is a more common and perhaps more intuitive representation of data, although a graph tends to lend itself less for the visualization and inspection of discrete data when things start to grow.

Example graph¶

Let's consider an example graph:

graph LR

  A --> B
  A --> C
  C --> A
  B --> D

Here you can see dependencies between four entities: A, B, C, and D.

A is input to B and C.
C provides input back to A.
B provides input to D.

Corresponding DSM¶

The corresponding DSM of this would be:

Matrix axis: nodes¶

The nodes are displayed on both axis, always in identical order (A, B, C, D) from the top-left to the bottom-right, with their rows and columns numbered from 1 onwards.

Matrix dots: edges¶

The inputs of a node, or its incoming edges are displayed in its row.
The outputs of a node, or its outgoing edges are therefore displayed in its column.
You can interpret the diagonal as the "self" of a node.
Any self-loops could be displayed here.
It is often greyed out for readability purposes.

For instance the blue dot in the first row (A) in the third column (C) corresponds to the arrow from C to A.

Info

This is called the IR/FAD convention, or Inputs in Rows/Feedback Above Diagonal. Note how the feedback from C to A is above the diagonal if you were to interpret the nodes on the axis as the steps of a process, for example.

Sometimes the transpose matrix is used (IC/FBD), but it is far less common and we usually stick to IR/FAD whenever we can.

So for the given dependencies in the graph's description that corresponds to:

A is input to B and C: column 1 to row 2 and 3.
C provides input back to A: column 3 to row 1.
B provides input to D: column 2 to row 4.