Software vulnerabilities, also known as flaws, bugs or weaknesses, are common in modern information systems, putting critical data of organizations and individuals at cyber risk. Due to the scarcity of resources, initial risk assessment is becoming a necessary step to prioritize vulnerabilities and make better decisions on remediation, mitigation, and patching. Datasets containing historical vulnerability information are crucial digital assets to enable AI-based risk assessments. However, existing datasets focus on collecting information on individual vulnerabilities while simply storing them in relational databases, disregarding their structural connections. This paper constructs a compact vulnerability knowledge graph, VulKG, containing over 276K nodes and 1M relationships to represent the connections between vulnerabilities, exploits, affected products, vendors, referred domain names, and more. We provide a detailed analysis of VulKG modeling and construction, demonstrating VulKG-based query and reasoning, and providing a use case of applying VulKG to a vulnerability risk assessment task, i.e., co-exploitation behavior discovery. Experimental results demonstrate the value of graph connections in vulnerability risk assessment tasks. VulKG offers exciting opportunities for more novel and significant research in areas related to vulnerability risk assessment. The data and codes of this paper are available at https://github.com/happyResearcher/VulKG.git .