Graphs are a popular data type found in many domains. Numerous techniques have been proposed to find interesting patterns in graphs to help understand the data and support decision-making. However, there are generally two limitations that hinder their practical use: (1) they have multiple parameters that are hard to set but greatly influence results, (2) and they generally focus on identifying complex subgraphs while ignoring relationships between attributes of nodes. Graphs are a popular data type found in many domains. Numerous techniques have been proposed to find interesting patterns in graphs to help understand the data and support decision-making. However, there are generally two limitations that hinder their practical use: (1) they have multiple parameters that are hard to set but greatly influence results, (2) and they generally focus on identifying complex subgraphs while ignoring relationships between attributes of nodes. To address these problems, we propose a parameter-free algorithm named CSPM (Compressing Star Pattern Miner) which identifies star-shaped patterns that indicate strong correlations among attributes via the concept of conditional entropy and the minimum description length principle. Experiments performed on several benchmark datasets show that CSPM reveals insightful and interpretable patterns and is efficient in runtime. Moreover, quantitative evaluations on two real-world applications show that CSPM has broad applications as it successfully boosts the accuracy of graph attribute completion models by up to 30.68% and uncovers important patterns in telecommunication alarm data.