science

Process graph

Process graph is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Process graph rather than just read about it. In short: In mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling. Description With a process graph, the vertices of the graph are of two types, operation (O) and material (M).

Key takeaways

Process graph belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Process graph to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Process graph from memory before moving on to harder problems.

Reference excerpt

In mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling.

Description With a process graph, the vertices of the graph are of two types, operation (O) and material (M). These vertex types form two disjunctive sets. The edges of the graph link the O and M vertices. An edge from an operation vertex (O) connects to a material vertex (M) if M is the output of O, such as a 'document' (material) that is output by a 'write-up' (operation). An edge from M to O indicates that M is an element of the input set of O, e.g. a document may be part of the input to a 'review' operation.

Applications Process-graph is in use in different fields of application in Process Network Synthesis (PNS) . An example for an application is Process Network Synthesis. The method is in scientific use to find optimum process chains in chemical formulas, energy technology networks and other optimisation problems like evacuation routes in buildings or transportation routes. Process graphs are also used in understanding the control flow of multi-threaded processes. If there are n concurrent threads running, a process graph models the execution of n concurrent threads and their trajectories through an n dimensional Cartesian plane. The origin of the graph corresponds to the initial state where none of the threads have completed an instruction. Each directed edge corresponds to the execution of an instruction and transition to other. Valid edges can either go up or right because programs cannot run backward for the edges to left or down. Since two threads can't complete the same instruction at the same time, diagonal edges are not allowed.

References

External links P-Graph wiki Process Network Synthesis Problem Definition

Worked examples

Example 1 — a first encounter with Process graph

Start with the simplest possible case. Write down what Process graph claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Process graph before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Process graph ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Process graph

In research: Process graph appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Process graph in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Process graph is common in secondary-school and first-year university syllabi. It links to neighbouring topics Application-specific graphs, so understanding it makes those chapters shorter.
In everyday life: Look for Process graph outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Process graph in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Process graph means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Process graph out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Process graph in simple terms?

In mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling. Description With a process graph, the vertices of the graph are of two types, operation (O) and material (M).

Why does Process graph matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Process graph?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Process graph.