  Complex network infrastructure systems for power-supply, communication, and
transportation support our economical and social activities, however they are
extremely vulnerable against the frequently increasing large disasters or
attacks. Thus, a reconstructing from damaged network is rather advisable than
empirically performed recovering to the original vulnerable one. In order to
reconstruct a sustainable network, we focus on enhancing loops so as not to be
trees as possible by node removals. Although this optimization is corresponded
to an intractable combinatorial problem, we propose self-healing methods based
on enhancing loops in applying an approximate calculation inspired from a
statistical physics approach. We show that both higher robustness and
efficiency are obtained in our proposed methods with saving the resource of
links and ports than ones in the conventional healing methods. Moreover, the
reconstructed network by healing can become more tolerant than the original one
before attacks, when some extent of damaged links are reusable or compensated
as investment of resource. These results will be open up the potential of
network reconstruction by self-healing with adaptive capacity in the meaning of
resilience.
