  The Large language models (LLMs) have showcased superior capabilities in
sophisticated tasks across various domains, stemming from basic question-answer
(QA), they are nowadays used as decision assistants or explainers for
unfamiliar content. However, they are not always correct due to the data
sparsity in specific domain corpus, or the model's hallucination problems.
Given this, how much should we trust the responses from LLMs? This paper
presents a novel way to evaluate the uncertainty that captures the directional
instability, by constructing a directional graph from entailment probabilities,
and we innovatively conduct Random Walk Laplacian given the asymmetric property
of a constructed directed graph, then the uncertainty is aggregated by the
derived eigenvalues from the Laplacian process. We also provide a way to
incorporate the existing work's semantics uncertainty with our proposed layer.
Besides, this paper identifies the vagueness issues in the raw response set and
proposes an augmentation approach to mitigate such a problem, we conducted
extensive empirical experiments and demonstrated the superiority of our
proposed solutions.
