Description: A symmetric graph is one where the edges are undirected and adjacency is mutual. This means that if there is a connection between two nodes, this connection is bidirectional, allowing traversal from one node to another in both directions without restrictions. Formally, a graph G is defined as an ordered pair (V, E), where V is a set of vertices and E is a set of edges. In a symmetric graph, for every edge (u, v) in E, there is also the edge (v, u). This symmetry property is fundamental in various applications, as it allows for the representation of relationships that do not have a specific direction, such as connections in a network or interactions in a system. Symmetric graphs are an important category within graph theory, which is a branch of mathematics and computer science that studies the properties and structures of graphs. Their simplicity and clarity in representing relationships make them a valuable tool for modeling and analyzing complex systems across various disciplines, from computer science to biology and sociology.
