Euler characteristic of a graph

The Euler characteristic of a graph is a number that helps describe its overall shape and structure. It is calculated using the formula: (Number of vertices) – (Number of edges) + (Number of faces). For planar graphs (those that can be drawn on a flat surface without crossing lines), this number remains constant and relates to the surface's properties. It provides insight into the graph’s connectivity and complexity, linking to topological properties. In essence, the Euler characteristic is a way to summarize a graph’s fundamental structure and how its components are interconnected.