Graph properties refer to the characteristics that define the structure and behavior of a graph, which is a collection of vertices (or nodes) connected by edges. Key properties include the number of vertices and edges, the degree of each vertex, and whether the graph is directed or undirected. These properties help in understanding how information flows within the graph and how connected the nodes are. Another important aspect of graph properties is connectivity, which indicates whether there is a path between any two vertices. Additionally, graphs can be classified as cyclic or acyclic, depending on whether they contain cycles. Understanding these properties is essential in fields like computer science, where graphs are used to model networks and relationships, such as in social networks or transportation systems.