Types of graphs

Graph Fundamentals: This topic explains the basic concepts of graphs such as vertices, edges, and degrees.

Graph Classification: This topic covers the classification of graphs based on different criteria such as the number of vertices, edges, cycles, bipartite graphs, etc.

Directed Graphs: It explains the directed graphs and its properties such as indegree, outdegree, strongly connected components, etc.

Weighted Graphs: This topic explains the concept of weights for graphs, also known as capacity or cost associated with edges.

Trees: This topic explains the concept of trees, which are special cases of graphs, having no cycles and the properties defining them.

Spanning Trees: It talks about the concept of spanning trees, which are trees that include all the vertices of the parent graph.

Planar Graphs: It introduces planar graphs and their properties, including Euler's formula.

Graph Coloring: This topic explains the concept of graph coloring, where a graph can be colored in such a way that no two adjacent vertices have the same color.

Matching Theory: It covers the concept of matching in graphs, where a matching is a set of edges with no common vertices.

Graph Algorithms: There are various algorithms associated with graphs, including Kruskal's algorithm, Prim's algorithm, Dijkstra's algorithm, etc.

Graph Connectivity: This topic explains connectivity in graphs, including concepts like strongly and weakly connected graphs.

Graph Traversals: This involves various methods to traverse a graph, such as depth-first search and breadth-first search.

Graph Isomorphism: It covers the concept of isomorphism in graphs, where two graphs are isomorphic if they have the same structure but different labels.

Spectral Graph Theory: It introduces the connection between the eigenvalues and eigenvectors of a graph's associated matrix and its properties, such as connectivity and number of cycles.

Random Graphs: This topic explains the concept of random graphs, where edges are added randomly based on certain probabilities or distributions.

Networks: It discusses the concept of networks, which usually involve graphs where vertices represent nodes or points, and edges represent connections or relationships between them.

Applications of Graph Theory: Graph theory has numerous applications in various fields, including computer science, social network analysis, transportation and logistics, etc.

Bar Graphs: These are the most common type of graph used to represent categorical data using rectangular bars.

Line Graphs: Line graphs are used to represent changes in data values over time by connecting individual data points with a continuous line.

Scatter Plots: Scatter plots are used to represent the correlation between two variables by plotting pairs of data points on a two-dimensional plane.

Pie Charts: Pie charts are used to represent proportions of a whole by dividing a circle into different segments.

Histograms: Histograms are similar to bar graphs, but they are used to represent continuous data by dividing it into intervals or bins.

Gantt Charts: Gantt charts are used to represent project schedules by displaying the timelines and dependencies of different project tasks and milestones.

Box Plots: Box plots are used to represent the distribution of data by depicting the median, quartiles, and outlier values in the form of a box and whisker plot.

Network Graphs: Network graphs are used to represent complex systems and their relationships by using nodes and edges to depict connections between different entities.

Heatmaps: Heatmaps are used to represent the intensity of certain types of data values by using a color gradient to represent different levels of concentration.

Radar Charts: Radar charts are used to represent multiple variables by plotting them all on a circular grid and connecting their respective data points.