Ybranch

Ybranch is a term used in graph theory and network analysis to describe a Y-shaped junction, formed when three paths meet at a single central point. In an undirected graph, this central point is a vertex of degree three, and the three incident edges lead to three distinct subpaths. The name reflects the resemblance to the letter Y.

In a tree, which is a connected acyclic graph, a Y-branch corresponds to an internal vertex of degree three. Depending on orientation, one may view this junction as splitting a single incoming path into two outgoing branches, or as a root with three branches. Y-branch nodes are the primary sources of branching complexity in such networks.

Y-branch motifs occur in various real-world networks, including river and drainage networks, vascular and neural trees, canal systems, and electrical or data networks where three components join at a junction. They are used in modeling to study flow, connectivity, and resilience, and in visualization to illustrate branching structure.

In analysis, a common operation is the detection and counting of Y-branch nodes by identifying vertices with degree three. Planarity, embedding, and geometry of arms can vary, but the combinatorial property—three incident edges at a single vertex—defines the Y-branch concept. See also: degree, branching, tree, graph theory.