Great video! It was clear and concise. One thing I noted, at 4:25, you highlighted (D, E, G, D) but wrote (D, G, E) on the screen. Thanks for all your hard work!!
Great question. The concept of walk/path/trail/cycle is introductory, but once we familiarize ourselves with those basic concepts, that's when the fun starts. The graph algorithms we build in terms of/based on them can be very useful in real life. Many real-world problems can be viewed from the perspective of finding the optimal path or trail in a network. Routing algorithms, like planning the most efficient route for a deliveryperson to follow, are one example, using walks in weighted graphs. Also, many phenomena in the world can be modeled as networks, and it's often useful to ask questions about these networks in terms of properties based on walks/trails/paths/cycles/circuits. For example, we can think of social networks, with people being the vertices, and adjacent when they are friends. The question we want to answer is who are the most influential people in that social network. Using the concept of paths (actually shortest paths) between vertices, we can attempt to quantify "influence". For each person, we can find all the shortest paths between that person and any other person in the network, take the average, and the people with the lowest averages could be said to be the most important people in the network, as they're the fewest average "steps removed" from others. This may not be the most accurate way to say who is the most influential, but there are other metrics of importance, some involving random walks, some may even involve cycles/circuits. This kind of measurement is known as centrality, I have a few videos about it if you're interested in learning more: ua-cam.com/video/HFP4Br7uvYo/v-deo.html, it has a bunch of uses and applications. Search engines use a much more complicated type of centrality to rank websites. And there are types of centrality that are used to model the spread of disease in a network of people or cities/states. All of these applications came from the basic building blocks of walks and paths in graphs. Hope this adds some context to these concepts.
![What are Eulerian Circuits and Trails? [Graph Theory]](http://i.ytimg.com/vi/2hH-TfcrUl8/mqdefault.jpg)
![What are Eulerian Circuits and Trails? [Graph Theory]](/img/tr.png)
![What are Hamiltonian Cycles and Paths? [Graph Theory]](/img/n.gif)
Thank you for watching! Let me know if you have any feedback or questions.
0:00 - Graph Walks
0:53 - Graph walks as lists
1:35 - Trails
2:50 - Circuits
3:30 - Paths
4:50 - Closed paths = Cycle
5:30 - Summary
6:44 - Real-world Example
7:35 - Traveling Salesman Problem
Great video! It was clear and concise. One thing I noted, at 4:25, you highlighted (D, E, G, D) but wrote (D, G, E) on the screen. Thanks for all your hard work!!
Good catch, thanks for letting me know and for the kind words 👍
Thank you sir, such a great concise explanation
Most welcome!
Thank you! this is fantastic.
on minute 4:39 there is a typo when it says (D,G,E) is a cycle, you should add D after the E.
Thank you.
is it possible to skip vertex in a trail? for example G>E>F>D???? anyone please? answer..
It is not allowed to skip vertices in a trail.
@@VitalSine Thanks for the clarification
Grandi soluzioni che amo.
Thanks. it helps me a lot
7:35 little error path abd has weight 5 = 3.5 , should be 5+3.5
Nice catch, thanks for letting me know 👍, I meant to display 5 + 3.5 there.
great video!
Thank you :)
Good video man thanks
Glad you enjoyed it!
Good video 👍🏿
Thank you!
thank you
how would this be useful for real life other than passing tests? or is it just pointless
Great question. The concept of walk/path/trail/cycle is introductory, but once we familiarize ourselves with those basic concepts, that's when the fun starts. The graph algorithms we build in terms of/based on them can be very useful in real life.
Many real-world problems can be viewed from the perspective of finding the optimal path or trail in a network. Routing algorithms, like planning the most efficient route for a deliveryperson to follow, are one example, using walks in weighted graphs.
Also, many phenomena in the world can be modeled as networks, and it's often useful to ask questions about these networks in terms of properties based on walks/trails/paths/cycles/circuits. For example, we can think of social networks, with people being the vertices, and adjacent when they are friends. The question we want to answer is who are the most influential people in that social network.
Using the concept of paths (actually shortest paths) between vertices, we can attempt to quantify "influence". For each person, we can find all the shortest paths between that person and any other person in the network, take the average, and the people with the lowest averages could be said to be the most important people in the network, as they're the fewest average "steps removed" from others. This may not be the most accurate way to say who is the most influential, but there are other metrics of importance, some involving random walks, some may even involve cycles/circuits. This kind of measurement is known as centrality, I have a few videos about it if you're interested in learning more: ua-cam.com/video/HFP4Br7uvYo/v-deo.html, it has a bunch of uses and applications.
Search engines use a much more complicated type of centrality to rank websites. And there are types of centrality that are used to model the spread of disease in a network of people or cities/states. All of these applications came from the basic building blocks of walks and paths in graphs. Hope this adds some context to these concepts.
@@VitalSine this helps explain the use a lot, thank you so much for the very in-depth reply.
i love you