Short-text clustering is crucial for extracting knowledge from online social media platforms. The task is challenging due to the limited text length and various forms of noise. Short texts about a specific topic often share common terms that are representative of a topic, known as topic-representative keywords. The goal is to identify these keywords by clustering at the word level. The short texts are represented as a word graph network where nodes represent words and edges represent co-occurrence or semantic relationships, capturing the context. We propose a novel centrality measure, Encoder Indexed Centrality (EIC), that is applied to the graph to identify the topic-representative keywords. The proposed metric is based on the latent representation of existing edge-weighted centrality measures. By measuring thematic closeness and semantic coherence, we discover semantically relevant word clusters around each keyword. This induced word cloud serves as the basis for short-text clustering. Our model, implemented on a short-text Twitter dataset, demonstrates superior performance compared to various baselines.