Nontechnical Summary of Research

Imagine how difficult navigating the web would be if the links between two websites had nothing to do with the content of the webpages, so that a website about the structure of the web could link to a website about salamanders. It would certainly make navigation more difficult. Unfortunately, many of the current models for the web and other social networks ignore the semantic aspects of these networks. Working with Scheinerman, I have extended the work of Kraetzl, Nickel, and Scheinerman [1], to develop a model for social networks in which the connections are influenced by the semantics of the network. The essence of this random model is to assign to each entity in the network random semantic content, and then, the probability of two entities having a connection increases as they become semantically close. Also, part of the semantic information encodes the “talkativeness” of each entity which also influences the connections. Scheinerman and I were able to show that this model has several typical properties of social networks [2]; namely that The friend of my friend is more likely to be my friend, and The infamous “6-degrees of Kevin Bacon” property. Kraetzl, et al. had already shown that there exists a way of distributing the semantic information such that the number of entities with a given number of connections falls within the observed behavior of social networks [1]. Now imagine searching the web for a particular website but without knowing anything about any website other than how many websites it points to, like a giant game of blind man’s bluff. Now imagine that instead of the fairly random web we have now, there was a slightly more structured web consisting of two parts, each looking like the current web, and there were only a very few links between them. The game of blind man’s bluff would be much harder on the second version of the web, because of the ability to remove very few edges and separate the web into two pieces. Building on my work with Scheinerman, I have shown that if such cuts exist in the semantic model, they must not have any semantic content. That is, in a certain sense, those cuts must arise by chance, rather than due to fundamental semantic information in the network. Recently I have also shown that there is a natural modification of this model to bring the expected number of a connections per entity more inline with the observed behavior of the web, and furthermore, this does not disturb any of the previously shown properties [3]. If I receive the Killam Postdoctoral Fellowship, I intend to work with Prof. Janssen and the research groups on Graphs and Games and Modelling and Mining of Networked Information Spaces to further the theoretical and practical applications of the semantic model. In particular, over the long term, I would like to work towards an understanding of how viruses spread on a network generated via this semantic model. The goal of this would be to exploit this understanding to develop new inoculation schemes for various networks, such as the Internet (for computer viruses). Along the way, there are two ancillary questions that need to be answered in order to fully realize the potential of the semantic model. First, is there an efficient means to take observations from a network, or a class of networks, and extract an appropriate semantic content so that the model accurately reflects the essential nature of the network(s)? Second, what would be the effect of a time-based evolution of the semantic content of vertices? Perhaps it is most obviously the case with human interaction, but when two entities interact it is natural that they should have some effect on each other, and that effect should be able to trickle out to other entities like ripples on a pond. As of right now, in the semantic and many other models for complex networks, there is no way to incorporate this evolution within the framework of the model. Regardless of the direction my research takes, I look forward to the opportunity to work with the faculty at Dalhousie University.