Graph (mathematics)

CategoriesCausal Wizard Concept , Graph , Data , Variables , Study Design , Independence

A mathematical graph is a visual representation of a set of objects and their connections through edges or arcs.

A mathematical graph is a visual representation of a set of objects, where some pairs of those objects are connected by links. These links are called edges or arcs, and the objects they connect are called vertices or nodes.

Graphs can be used to represent a wide range of mathematical structures, including social networks, transportation systems, chemical molecules, and more. They are commonly used in computer science, operations research, and other fields to model relationships between different entities.

Types of Graph

There are many types of graphs, including directed graphs, undirected graphs, weighted graphs, and bipartite graphs, among others.

  • Directed graphs have edges that point in a specific direction, while undirected graphs do not.
  • Weighted graphs assign a numerical value to each edge, representing some sort of cost or benefit associated with traversing that edge.
  • Bipartite graphs have two sets of vertices, and edges only connect vertices from one set to vertices from the other set.
  • A Graphical Model is a graph which additionally captures probabilistic relationships among its vertices, which are assumed to be random variables.

Properties of Graphs

Graph theory is a branch of mathematics that studies the properties of graphs and their applications. It has numerous applications in computer science, including in the design and analysis of algorithms, the study of network flows, and the modeling of complex systems.

Some of the important concepts in graph theory include connectivity, paths, cycles, and subgraphs.

  • Connectivity refers to how easily (or whether it is possible) to travel from one vertex to another
  • Paths are sequences of edges that connect two or more vertices in the graph.
  • Cycles are paths which revisit a vertex
  • Subgraphs are smaller graphs that are contained within the larger graph.

Graph vs tabular models

The concept of a mathematical graph provides a powerful tool for modeling and analyzing complex systems, particularly network systems, which includes road, rail and pipe network infrastructure as well as computer or telecommunications networks. Graphs are typically used when the main alternative - tabular data, or relational data - is inconvenient or inappropriate.

In Causal Wizard

Graphs are important in causal wizard, because you will provide your domain knowledge in the form of a Causal Diagram, a type of graph which defines causal relationships between variables.

Related articles
In categories