Before revision: The interest in spatial networks where vertices are embedded in a one-dimensional space is growing. Remarkable examples of these networks are syntactic dependency trees and RNA structures. In this setup, the vertices of the network are arranged linearly and then edges may cross when drawn above the sequence of vertices. Recently, two aspects of the distribution of the number of crossings in uniformly randomlinear arrangements have been investigated: the expectation and the variance.
After revision: The crossing number, i.e. the minimum number of edge crossings arising when drawing a graph on a certain surface, is a very important problem of graph theory. The opposite problem, i.e. the maximum crossing number, is receiving growing attention. Here we consider a complementary problem of the distribution of the number of edge crossings, namely the variance of the number of crossings in uniformly randomlinear arrangements have been investigated: the expectation and the variance.