Difference between random, cycle graph, bipartite, lattice, real netwrok, configuration model

What is the difference between random, cycle graph, bipartite, lattice, real netwrok, configuration model

Random Graph: A random graph is a type of mathematical object known as a graph, which is composed of vertices (or nodes) and edges (lines connecting the vertices). In a random graph, the presence of an edge between any two nodes is determined randomly. The most common type of random graph is the Erdős–Rényi model. In an Erdős–Rényi graph, each edge has a fixed probability of being present or absent, independently of the other edges. Cycle Graph: A cycle graph is a graph that consists of a single cycle - a path of edges and vertices wherein a vertex is reachable from itself. So, all the vertices and edges form a closed loop with no loose ends. An example of a cycle graph would be a circular graph where each node is connected to two other nodes, forming a ring-like structure. Bipartite Graph: A bipartite graph is a type of graph that has its vertices divided into two disjoint sets. All edges in the graph connect a vertex from the first set to a vertex in the second set. In other words, no edge within the same set of vertices exists. An example would be a graph representing people and their hobbies, where an edge connects a person to a hobby they enjoy, but people don't directly connect to other people, and hobbies don't connect to other hobbies. Lattice Graph: A lattice graph is a graph that can be drawn in the Euclidean space such that all its vertices are in a regular grid. The most common examples of lattice graphs are the square grid graph and the triangular grid graph. Real Network: Real networks, or real-world networks, refer to graphs that represent actual systems in our world. These could be the internet (nodes as webpages, edges as links), social networks (nodes as people, edges as friendships), transportation networks (nodes as locations, edges as roads), and more. These networks often exhibit complex and interesting properties that aren't necessarily seen in simpler types of graphs. For example, they may exhibit "small-world" properties (most nodes can be reached from others in a small number of steps), or they may have a "scale-free" degree distribution (most nodes have few connections, but a few nodes have many connections). Configuration Model: The configuration model is a method of generating random graphs with a specified degree sequence. In other words, you can specify how many edges you want each node in your graph to have, and the configuration model will generate a random graph with that property. Note that this model doesn't necessarily generate simple graphs; it can sometimes produce graphs with multiple edges between the same pair of nodes, or nodes with an edge to themselves.