  The importance of effective detection is underscored by the fact that
socialbots imitate human behavior to propagate misinformation, leading to an
ongoing competition between socialbots and detectors. Despite the rapid
advancement of reactive detectors, the exploration of adversarial socialbot
modeling remains incomplete, significantly hindering the development of
proactive detectors. To address this issue, we propose a mathematical
Structural Information principles-based Adversarial Socialbots Modeling
framework, namely SIASM, to enable more accurate and effective modeling of
adversarial behaviors. First, a heterogeneous graph is presented to integrate
various users and rich activities in the original social network and measure
its dynamic uncertainty as structural entropy. By minimizing the
high-dimensional structural entropy, a hierarchical community structure of the
social network is generated and referred to as the optimal encoding tree.
Secondly, a novel method is designed to quantify influence by utilizing the
assigned structural entropy, which helps reduce the computational cost of SIASM
by filtering out uninfluential users. Besides, a new conditional structural
entropy is defined between the socialbot and other users to guide the follower
selection for network influence maximization. Extensive and comparative
experiments on both homogeneous and heterogeneous social networks demonstrate
that, compared with state-of-the-art baselines, the proposed SIASM framework
yields substantial performance improvements in terms of network influence (up
to 16.32%) and sustainable stealthiness (up to 16.29%) when evaluated against a
robust detector with 90% accuracy.
