  The evolution of complex networks is governed by both growing rules and
internal properties. Most evolving network models (e.g. preferential
attachment) emphasize on the growing strategy, while neglecting the
characteristics of individual nodes. In this study, we analyzed a widely
studied network: the evolving protein-protein interaction (PPI) network. We
discovered the critical contribution of individual nodes, occurring
particularly at their birth. Specifically, a node is born with a fitness value
- a measurement of its intrinsic significance. Upon the introduction of a node
with a large fitness into the network, a corresponding high birth-degree is
determined accordingly, leading to an abrupt increase of connectivity in the
network. The degree fraction of these large (hub) nodes does not decay away
with the network evolution, while keeping a constant influence over the
lifetime. Here we developed the birth-burst model, an adaptation of the fitness
model, to simulate degree-burst and phase-transition in the network evolution.
