Planarity

Planarity refers to whether a graph—a collection of points (vertices) connected by lines (edges)—can be drawn on a flat surface without any of the lines crossing each other. A planar graph can be represented on a plane so that its edges only touch at their endpoints. If it's impossible to draw the graph without some crossing lines, the graph is non-planar. This concept helps in areas like circuit design and map-making, where minimizing crossings leads to clearer and more efficient layouts. In essence, planarity measures how neatly a complex network can be organized on a flat surface.