1. Graphs Concept

A Graph is a non-linear data structure consisting of nodes and edges . The nodes are formally called vertices, and the edges are lines or arcs that connect any two nodes in the graph. 
 Graphs are used to solve many real-world problems. They are used to represent networks, such as social networks, transportation networks (roads and cities), or computer networks. 
 1.1 Graph Terminology 
 
 Vertex (or Node): The fundamental unit of the graph. 
 Edge: A line that connects two vertices. 
 Path: A sequence of vertices connected by edges. 
 Cycle: A path that starts and ends at the same vertex. A graph with no cycles is acyclic. 
 Connected Graph: An undirected graph where there is a path between any two vertices. 
 Weighted Graph: Each edge is assigned a numerical value or "weight," often representing cost or distance. 
 Unweighted Graph: Edges do not have weights. 
 
 1.2 Graph Analogy 
 Imagine a social network like Facebook or Twitter. 
 
 Each person is a Vertex (Node) . 
 The friendship or connection between two people is an Edge . 
 If the friendship is mutual (i.e. Facebook), it's an undirected graph. 
 If you can "follow" someone without them following you back (i.e. Twitter), it's a directed graph. 
 
 1.3 Types of Graph 
 1.3.1 Undirected Graph 
 
 In an Undirected Graph , edges represent a mutual, bidirectional relationship. An edge (u, v) is identical to an edge (v, u) . There is no "direction" to the connection. 
 
 Analogy: A friendship on Facebook or a two-way street. If A is friends with B , then B is automatically friends with A . 
 Degree: The "degree" of a vertex is simply the total number of edges connected to it. 
 
 1.3.2 Directed Graph 
 
 In a Directed Graph (or Digraph) , edges are one-way streets. An edge (u, v) represents a connection from u to v , but it does not imply a connection from v to u . 
 
 Analogy: Following someone on Twitter or a one-way street. A can follow B (an edge A -> B ), but B does not have to follow A back. An edge B -> A would be a separate, distinct edge. 
 Degree: Degree is split into two types:
 
 In-degree: The number of edges pointing to the vertex. 
 Out-degree: The number of edges pointing away from the vertex.