Abstract
Studying the dynamics of information flow over social networks is important in understanding the rate and extent of the diffusion of innovations, the propagation of news and fake news, the proliferation of rumors, and the spread of infectious diseases. The learnings from such an endeavor can be used for new product sales forecasting, forecasting sales of an existing product in a new market, and controlling the rate and extent of information and disease propagation. This research focuses on the diffusion of innovations and first establishes how the structural properties of a large social network such as its size, connectivity, clustering, assortativity, centralization, and distance impact the rate and extent of the diffusion of innovations that takes place on it. We find that, in the case of the Bass diffusion model and everything else being the same, • The size of the network impacts the rate and extent of diffusion. The larger networks show a higher standardized net present value (NPV) of diffusion. • The variance in the degree distribution impacts the rate, and extent of diffusion; higher variability (as measured through lower degree centralization) increases the NPV. • The degree of clustering (measured through mean coreness) impacts the rate and extent of diffusion. Higher clustering increases the NPV. • Homophily, measured through degree assortativity increases the NPV. Other factors such as smaller average distance among nodes and denser connectivity also increase the NPV. These are important findings, especially because prior research has seldom paid attention to the size of the network and the pattern of connectivity (coreness and degree assortativity) between nodes. The network metrics such as average path length and the density of connection have a non-linear relationship with the network size, and networks having the same average path length can have very different patterns of connectivity. The research relies on computational experiments that have been conducted on large simulated networks and validations that have been conducted on large real social networks. The modeling and analysis of a large network are computationally expensive and time-intensive. Hence, this research also provides scalable and fast algorithms for simulating and analyzing large social networks. Specifically, this research involved • The development of a statistical software package fastnet that reduces the computational time by combining the efficient representation of a network and distributed computing. fastnet has been developed as an open-source R package and provides algorithms for estimating several (16 properties spanning six categories) structural properties of large networks. • The development of a network partitioning algorithm that makes the handling of the large network datasets possible when there are memory constraints, and the distributed computing more time-efficient. The research also yielded two algorithms called DC (Degree-Constraint) and CA (Cluster-Affiliation), to simulate realistic social networks. Existing social network simulation algorithms such as those proposed by Leskovec, Kleinberg, and Faloutsos (2005) do not capture several nuances of a real social network, but DC and CA do. These algorithms were used to create realistic social networks that served as the experimental testbeds for the studies of diffusion dynamics over social networks.