science

Multiple edges

Multiple edges 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 Multiple edges rather than just read about it. In short: In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or in a directed graph, two or more edges with both the same tail vertex and the same head vertex. A simple graph has no multiple edges and no loops.

Key takeaways

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

Reference excerpt

In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or in a directed graph, two or more edges with both the same tail vertex and the same head vertex. A simple graph has no multiple edges and no loops. Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops):

Where graphs are defined so as to allow multiple edges and loops, a graph without loops or multiple edges is often distinguished from other graphs by calling it a simple graph. Where graphs are defined so as to disallow multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which can have multiple edges. Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view. Additionally, they constitute the core differentiating feature of multidimensional networks. A planar graph remains planar if an edge is added between two vertices already joined by an edge; thus, adding multiple edges preserves planarity. A dipole graph is a graph with two vertices, in which all edges are parallel to each other.

Notes

References Balakrishnan, V. K.; Graph Theory, McGraw-Hill; 1 edition (February 1, 1997). ISBN 0-07-005489-4. Bollobás, Béla; Modern Graph Theory, Springer; 1st edition (August 12, 2002). ISBN 0-387-98488-7. Diestel, Reinhard; Graph Theory, Springer; 2nd edition (February 18, 2000). ISBN 0-387-98976-5. Gross, Jonathon L, and Yellen, Jay; Graph Theory and Its Applications, CRC Press (December 30, 1998). ISBN 0-8493-3982-0. Gross, Jonathon L, and Yellen, Jay; (eds); Handbook of Graph Theory. CRC (December 29, 2003). ISBN 1-58488-090-2. Zwillinger, Daniel; CRC Standard Mathematical Tables and Formulae, Chapman & Hall/CRC; 31st edition (November 27, 2002). ISBN 1-58488-291-3.

Illustrations

Multiple edges: Multiple edges joining two vertices. — Multiple edges joining two vertices.

Worked examples

Example 1 — a first encounter with Multiple edges

Start with the simplest possible case. Write down what Multiple edges 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 Multiple edges 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 Multiple edges 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 Multiple edges

In research: Multiple edges 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 Multiple edges 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: Multiple edges is common in secondary-school and first-year university syllabi. It links to neighbouring topics Graph theory objects, so understanding it makes those chapters shorter.
In everyday life: Look for Multiple edges 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 Multiple edges in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Multiple edges 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 Multiple edges out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Multiple edges in simple terms?

Why does Multiple edges 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 Multiple edges?

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 Multiple edges.