Expectation and Variance of Self-assembled Graph Structures

Understanding how nanostructures are self-assembled into more complex forms is a crucial component of nanotechnology that shall lead towards understanding other processes and structures in nature. In this paper we use a model of self-assembly using flexible junction molecules and describe how it can in some static conditions be used to predict the outcome of a graph self-assembly. Using probabilistic methods, we show the expectation and the variance of the number of self-assembled cycles, K3, and discuss generalization of these results for Cn. We tie this analysis to previously observed experimental results.