Molecular processes of fiber formation and network genesis in polyethylene (PE) are studied by molecular dynamics simulation of crystallization from highly stretched melt. We consider a system comprising 150 molecules of 500 united atoms, which is much larger than that of our previous work on fiber structures and their deformation [Polymer 2013, 54, 3086], aiming to study crystal nucleation and growth separately. Rapid elongation of the isotropic melt gives rise to incipient crystal clusters or embryos much smaller than critical nuclei. Subsequent isothermal crystallization of the stretched melt leads to three distinct stages of structure formation. The initial stage is a period waiting for critical nucleation. In the second stage that follows, we observe independent growth of isolated lamellae and resulting polynomial increases in crystallinity. In the last stage the crystals come to collide with each other to give well-aligned stacked lamellae. By dividing the system into mesh cells (pixels) and using an algorithm for image processing, we analyze the growth of clusters in detail in terms of their sizes and shapes. Despite highly anisotropic chain conformation in the melt, we find rather isotropic growth of the clusters both along and perpendicular to the fiber axis in the early stage of crystallization, where crystallites show linear growth of similar rate for each direction. The exception is the crystallization under high tension, where lateral growth of lamellae seems to be hindered indicating characteristic diffusion-controlled growth. We also study genesis and development of polymer network in situ by properly defining fold, tie, and cilium segments connected to the growing crystallites. In the early stage of the network genesis, small crystal clusters are connected to very long cilia which are forming the dominant component of the system. In the following stage of network development, where the crystallites show marked growth in size, the long cilia are rapidly reeled into the crystalline region, and the folds and ties are continually tightened. Through statistical analyses of the folds and ties during crystallization, we find that both of them are initially slack and have broad length distributions, but they continually tighten and come to have characteristic asymptotic distributions. Of special interest is that the tie molecules have rather stretched conformation even after sufficiently long crystallization, which is an indication of memory of crystallization process from the highly stretched melt.