Flow, process and networks
Markov-state transition diagram
Shows states and conditional transition probabilities in a Markov model.
- Diagram
- Transition
- Relationship
What it answers
How can a process move between states?
- Shape
- State nodes and probability-labelled arrows
- What it shows
- State persistence, cycles and absorbing states.
Example
The question
How do customers move between active, at risk and lost each month?
Monthly chance of moving between customer statuses (state diagram)
Illustrative data. It belongs to no company.
When to use it
Use it when
Communicating a small Markov model.
Avoid it when
Large state spaces or treating probabilities as guaranteed paths.
How to read it
Follow probability-labelled arrows from the current state.
Note
Define the time step and model assumptions.
The data you need
- Layout
- Transition edge list
- Fields
- FromState: text; ToState: text; Probability: number in [0,1]
- One row is
- One state-to-state transition probability. What is the grain?
- Rules
- For a row-stochastic model, sum probabilities to 1 for each FromState. Include absorbing-state self-transitions.
- Optional
- Alternative transition counts with a documented normalisation.
- Preparation
- Build valid state probabilities for a defined time step; check each outgoing-state total and absorbing self-loops.
- Units
- Arrows show probabilities conditional on the current state and defined next-step interval; outgoing probabilities sum 1.
Worked example
A->A0.8, A->B0.2. Draw a self-loop and outgoing arrow; probabilities from A total 1.
| FromState | ToState | Probability |
|---|---|---|
| A | A | 0.8 |
| A | B | 0.2 |
| B | A | 0.3 |
| B | B | 0.7 |