Graph Theory in Networks (Applied)
Social, transport and web graphs.
Key idea
Social, transport and web graphs.
In depth
Real networks (social, web, transport) are graphs with weights and directions. Measures include degree, centrality, clustering and shortest paths. Methods such as PageRank and community detection extract structure.
Worked example
In a social network, the person with the highest degree has the most friends, but not necessarily the most influence.
Real-world uses
- Analysing friendships on social networks, transport systems and the structure of the web
Common mistake
Treating all high-degree nodes as most central.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Graph Theory in Networks (Applied)?
Social, transport and web graphs. It is a topic at the expert level in Differential Equations, Abstract Algebra & Applied Math.
Where is Graph Theory in Networks (Applied) used in real life?
Real-world examples: Analysing friendships on social networks, transport systems and the structure of the web.
What should I learn before Graph Theory in Networks (Applied)?
Make sure you are comfortable with Lie Groups and Lie Algebras, the previous topic in Differential Equations, Abstract Algebra & Applied Math.
What is a common mistake with Graph Theory in Networks (Applied)?
Treating all high-degree nodes as most central.
How can I practise Graph Theory in Networks (Applied)?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Graph Theory in Networks (Applied)?
Move on to Machine Learning Mathematics next.
Related expert topics in Differential Equations, Abstract Algebra & Applied Math
- Exact Equations – M dx + N dy = 0 with Mᵧ = Nₓ.
- Bernoulli Equations – Substitute v = y¹⁻ⁿ to linearise.
- Runge–Kutta Methods – Higher-accuracy numerical solvers.
- Second-Order Homogeneous Equations – Use the characteristic equation.
- Undetermined Coefficients – Guess the particular solution form.
- Variation of Parameters – General method for particular solutions.