  In graph theory and network analysis, node degree is defined as a simple but
powerful centrality to measure the local influence of node in a complex
network. Preferential attachment based on node degree has been widely adopted
for modeling network growth. However, many evidences exist which show deviation
of real network growth from what a pure degree-based model suggests. It seems
that node degree is not a reliable measure for predicting the preference of
newcomers in attaching to the network, or at least, it does not tell the whole
story. In this paper, we argue that there is another dimension to network
growth, one that we call node "coreness". The new dimension gives insights on
the global influence of nodes, in comparison to the local view the degree
metric provides. We found that the probability of existing nodes attracting new
nodes generally follows an exponential dependence on node coreness, while at
the same time, follows a power-law dependence on node degree. That is to say,
high-coreness nodes are more powerful than high-degree nodes in attracting
newcomers. The new dimension further discloses some hidden phenomena which
happen in the process of network growth. The power of node degree in attracting
newcomers increases over time while the influence of coreness decreases, and
finally, they reach a state of equilibrium in the growth. All these theories
have been tested on real-world networks.
