As the average degree \( \langle k \rangle \) of an Erdős-Rényi random network increases, the network's topology undergoes distinct phases of evolution. Which of the following statements accurately characterizes the network exactly at its critical point (\( \langle k \rangle = 1 \) )?
A) The size of the largest component scales as \( N^{2/3} \), containing a vanishing fraction of all nodes, and the cluster size distribution follows a power law.
B) The network lacks a giant component, and the size of the largest cluster scales logarithmically with the total number of nodes.
C) A giant component emerges that contains a finite fraction of the network's nodes, and the distribution of cluster sizes is exponential.
D) The giant component absorbs all isolated nodes and clusters, rendering the network fully connected.
E) None of the above.
Original idea by: João Vianini
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