  In social dilemmas, most interactions are transient and susceptible to
restructuring, leading to continuous changes in social networks over time.
Typically, agents assess the rewards of their current interactions and adjust
their connections to optimize outcomes. In this paper, we introduce an adaptive
network model in the snowdrift game to examine dynamic levels of cooperation
and network topology, involving the potential for both the termination of
existing connections and the establishment of new ones. In particular, we
define the agent's asymmetric disassociation tendency toward their neighbors,
which fundamentally determines the probability of edge dismantlement. The
mechanism allows agents to selectively sever and rewire their connections to
alternative individuals to refine partnerships. Our findings reveal that
adaptive networks are particularly effective in promoting a robust evolution
toward states of either pure cooperation or complete defection, especially
under conditions of extreme cost-benefit ratios, as compared to static network
models. Moreover, the dynamic restructuring of connections and the distribution
of network degrees among agents are closely linked to the levels of cooperation
in stationary states. Specifically, cooperators tend to seek broader
neighborhoods when confronted with the invasion of multiple defectors.
