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Visualizing relationships in Hierarchical Small World Networks


Antoun Yaacoub, Ali Awada, May Dehayni


Vol. 10  No. 6  pp. 71-79


This research provides a method for studying and visualizing different types of relationships in various worlds such as dictionaries and Web pages. As a first step, we identify different types of relationships between objects of the universes previously mentioned. The second step consists in developing a method to quantify the relationship to study. The constituents of the universe (Web pages, items associated with entries in a dictionary ...) form a HSWN graph (hierarchical small world network) whose nodes are entities and edges reflect a direct link (hypertext, definitional ...) between two nodes. This leads to introduce a method for studying the structure of large graphs of hierarchical small world type. Our approach is based on the use of Markovian matrices. A matrix is multiplied k times in order to quantify the relationship between all the nodes of the graph. To illustrate this approach, examples and results on Web and linguistic graphs are given.


Graph, Hierarchical small world network, link structure, synonymy, visualization