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-: Hey there. Eden here.

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And before we dive to LangGraph,

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I wanted to cover two important theoretical concept

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and terminologies we're going to be using constantly

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in this course.

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The first one is going to be graph, the data structure,

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and the other is going to be state machine.

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A graph is a mathematical object

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that helps us represent relationships.

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It consists of nodes, also known as vertices and edges

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that connect those nodes.

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Graph data structures are incredibly versatile

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and they can be used in a wide range of applications

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across different fields.

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We can use graphs to describe social networks,

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transportation maps between cities and roads

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and routes between cities.

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And what's cool about it is that in computer science

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there is a lot of research on this data structures

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and a lot of algorithms and property extraction

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of those graphs that help us solve a lot of problems

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in the real world.

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Just as a side note, as a software engineer,

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I used to work a lot with graph databases,

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working for cybersecurity companies,

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leveraging graphs to find and describe attack vectors

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of cloud assets on public clouds like AWS, GCP, and Azure,

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and also describe the connectivity

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of those assets on those clouds.

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To ask a question, is this web server internet-facing

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and is it connecting into a database,

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helping the cloud security posture management?

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By the way, I'll leave in the videos resources,

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a talk I gave about this topic in Minsk,

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you know, Python Developer Meetup discussing this topic

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in case this interests you.

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And if we want to geek out a little bit,

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we can see even the formal definition of a graph,

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the mathematical definition where a graph G or V and E

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comprised of V, a set of vertices and E, a set of edges

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described with a pair X and Y

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where X and Y belongs to the vertices set.

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And in case you got worried, then this is the last time

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we will see math in this course.

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So, let's continue.

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And a state machine on the other hand

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is a model of computation where it consists of states

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and transition between those states.

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And by defining different states

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and the rules for the transition between them,

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then the states can manage complex conditions

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and sequence in software systems.

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And now you can notice that state machines

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can be represented as graphs

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where the states are nodes and the transitions are edges.

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And this visualization helps us understanding

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the flow of the state machines

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and to manage their complexity.

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And here enters LangGraph,

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a powerful library built on top of LangChain.

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And with LangGraph we can describe our flows

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using those nodes and edges,

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and we can build very powerful

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and sophisticated agentic applications using it.

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And we'll see in the course that we'll be describing

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some very advanced and sophisticated agents,

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and it will be very easy to write them

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in LangGraph and to run them.

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And that's it for this video.

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I think it was important to have an alignment

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of what's a graph and what's a state machine

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before we dive into Flow Engineering and to LangGraph.