  The shell structure holds significant importance in various domains such as
information dissemination, supply chain management, and transportation. This
study focuses on investigating the shell structure of hub and non-hub nodes,
which play important roles in these domains. Our framework explores the
topology of Erd\"{o}s-R\'{e}nyi (ER) and Scale-Free (SF) networks, considering
source node selection strategies dependent on the nodes' degrees. We define the
shell $l$ in a network as the set of nodes at a distance $l$ from a given node
and represent $r_l$ as the fraction of nodes outside shell $l$. Statistical
properties of the shells are examined for a selected node, taking into account
the node's degree. For a network with a given degree distribution, we
analytically derive the degree distribution and average degree of nodes outside
shell $l$ as functions of $r_l$. Moreover, we discover that $r_l$ follows an
iterative functional form $r_l = \phi(r_{l-1})$, where $\phi$ is expressed in
terms of the generating function of the original degree distribution of the
network.
