An important task for Homeland Security is the prediction of threat vulnerabilities, such as through the detection of relationships between seemingly disjoint entities. A structure used for this task is a "semantic graph", also known as a "relational data graph" or an "attributed relational graph". These graphs encode relationships as "typed" links between a pair of "typed" nodes. Indeed, semantic graphs are very similar to semantic networks used in AI. The node and link types are related through an ontology graph (also known as a schema). Furthermore, each node has a set of attributes associated with it (e.g., "age" may be an attribute of a node of type "person"). Unfortunately, the selection of types and attributes for both nodes and links depends on human expertise and is somewhat subjective and even arbitrary. This subjectiveness introduces biases into any algorithm that operates on semantic graphs. Here, we raise some knowledge representation issues for semantic graphs and provide some possible solutions using recently developed ideas in the field of complex networks. In particular, we use the concept of transitivity to evaluate the relevance of individual links in the semantic graph for detecting relationships. We also propose new statistical measures for semantic graphs and illustrate these semantic measures on graphs constructed from movies and terrorism data.
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