others, a fact that agrees with evidence on the existence of a few cells with large plasticity potential. As this potential is rapidly lost after 40 days, cell types change their development ability in favor of the organism life maintenance. 

The fact that the average degree is close to 2 implies that the dynamical evolution of NHCD can be described by a critical branching process where every node has a certain probability of generating offsprings, in which case the critical condition for the branching to continue is 〈 k 〉 = 2 [31]. This effectively means that each node needs to give at least one descendant in order for the network to keep growing. If 〈 k 〉 < 2, the growth would stop early, while for 〈 k 〉 > 2 the growth would be faster than exponential. 

The network reaches the condition of criticality, 〈 k 〉 ≈ 2, at around t$_{∗}$ = 40 days (Fig. 4d) in conjunction with the transition from plasticity to functional behavior. After this, the average degree remains just above criticality to sustain a growth rate that guarantees the network survival. The majority of the nodes propagate the growth in a single line, but there are nodes which generate significantly more descendants to generate the diversity implied by the power-law distributions of degree and modularity. 

## II. DISCUSSION 

In summary, we present the first large-scale study of the prenatal evolution of the human cell differentiation process from the fertilized egg to a developed human. The process of human cell differentiation can be mapped onto a complex network composed of cell types and differentiation steps. This mapping allows us to study the cell differentiation process with state of the art network theory for community detection with the goal of identifying hitherto unknown functional relations between cell types. 

We discover a dynamical law of critical branching explaining the emergence of the network topology, which reveals a novel scale-invariant modular structure of the network of cell types. 

The self-similar modular features evidenced in Figs. 1, 2 and 3 are established early in the process and remain invariant during the evolution of the NHCD, although the network size changes significantly. 

Using this law, we are able to observe the network at different scales. The emerging picture clearly identifies clusters of cell types, or modules, and their connectivity to other modules within its own and other functions. The resulting hierarchical organization consists 

