Graph Theoretic Analyses of Semantic Networks:
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(for more information, see working paper: PDF, PS) OverviewSemantic networks are useful tools as representations for semantic knowledge and inference systems. Historically, semantic networks bring to mind the classic network theory of Collins and Quillian (1969) in which concepts are represented as hierarchies of interconnected nodes with nodes linked to certain attributes. In this research, the goal is to understand the large-scale organization of semantic networks. By applying graph-theoretic analyses, the large scale structure of semantic networks can be specified by distributions over a few variables, such as the length of the shortest path between two words and the number of connections per word. We show that these distributions display similar, nontrivial patterns for several semantic networks constructed by different means. We then argue that these regularities place strong constraints on the developmental principles by which connections between words are formed, and we propose a simple framework for modeling the acquisition and decay of semantic knowledge which is consistent with these constraints. In particular, we will show that the large-scale organization of semantic networks reveals a small-world structure that is very similar to the structure of several other real-life networks such as the neural network of the worm C. elegans, the collaboration network of film actors and the WWW. In addition, we will propose a new network model that mimics the global organization of semantic networks. This network acquires new concepts over time and connects these concepts preferentially to existing concepts that are rich in connections to other concepts. Two predictions follow from the model. First, because new concepts are preferentially attached to rich concepts, the distribution of the connectivity follows a power-law: some concepts have a connectivity that is orders of magnitude larger than the average concept. A related prediction is that semantic networks are scale-free: as the learner adds new concepts to the network, the distribution of the connectivity remains a power-law with the same shape. Second, because the model builds the representation of new concepts on older concepts, the order in which concepts are learned is important. The model predicts that concepts that are learned early in life should show higher connectivity and should be more resistant to memory disorders. We will show how this growth model can predict effects related to age of acquisition and how it might be utilized in models for semantic memory disorders such as semantic dementia. |
 Figure 1. Illustration of the growing network model. Concepts are added as nodes to the semantic network which are then integrated into the network by preferential attachment to existing concepts with rich connectivity while at the same time preserving the local neighborhood structure.
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