Network Intervention for Mental Disorders with Minimum Small Dense Subgroups

According to the literature in psychology, the existence of small dense subgroups is closely related to many mental illnesses, such as depression, bullying, and psychotic disorders. Here, small dense subgroups refer to the small groups in the social network in which members are socially dense but have no or few links to other individuals outside the group. Therefore, in this article, we make the first attempt to address the issue of small dense subgroups with the concept of
network intervention
from Psychology. We first introduce the new notion of
$\Delta$
-Subgroups (
$\Delta$
-SGs) to quantify the small dense subgroups. Then, following the concept of network intervention, we formulate a new research problem,
Small Subgroup Maximum Reduction Problem (SSMP)
, to reduce the number of small dense subgroups (i.e.,
$\Delta$
-SGs) in the social network. We prove that SSMP is NP-Hard and propose a linear-time algorithm, namely
3-SMMTG
, to find the optimal solution for a special case of SSMP with
$\Delta =3$
. We then devise a
$\frac{1}{2}(1-\frac{1}{e})$
-approximation algorithm, namely
ESGR
, for the general SSMP and enhance its efficiency with effective pruning methods. We conduct a 8-week evaluation study with 812 participants to validate the proposed SSMP and ESGR. The results show that the participants with the network intervention recommended by ESGR have significant improvements on Internet addiction and depression, as compared to those individuals without any intervention. We also perform experiments on 7 real datasets, and the experimental results manifest that the proposed algorithms outperform the other baselines in both efficiency and solution quality.