A comprehensive study of multiplicative attribute graph model

Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution.

ProjectION: Investigation Operative Networks

Corporations and enterprises have embraced the notion of shared experiences and collective workplaces by incorporating coworking places. A great deal of the methodology carries from the studio culture that architecture schools foster as well as think tank culture. Maker spaces and incubator spaces are prime examples of places that engender creative thought and products. This thesis seeks to explore the impact that architecture has on collaborative spaces with a focus on augmenting to their generated learning and design activities. The investigation explores the collaborative design process as a series of interactions between groups of individuals. This involves the impact of technology and its implications on those interactions. The goal of this thesis is not to further the use of a tool or systematic procedure, but to use architecture as a framing device to form places for collaborative processes.