  The degree-degree correlation is crucial in understanding the structural
properties of and dynamics occurring upon network, and is often measured by the
assortativity coefficient $r$. In this paper, we first study this measure in
detail and conclude that $r$ belongs to an asymmetric range $[-1,1)$ rather
than the widely-cited $[-1,1]$. Among which, we verify that star is the unique
tree network that achieves the lower bound of index $r$. Next, we obtain that
all the resultant networks based on several widely-used kinds of edge-based
iterative operations are disassortative if seed model has negative $r$, and
also generate a family of growing neutral networks. Then, we propose an
edge-based iterative operation to construct growing assortative network when
seed is assortative, and further extend it to work well in general setting.
Lastly, we establish a sufficient condition for existence of neutral tree
network, accordingly, not only find out a representative of any order neutral
tree network for the first time, but also are the first to create growing
neutral tree networks as well. Also, we obtain $8n/9$ neutral non-tree graphs
of distinct order as $n\rightarrow\infty$.
