Abstract:

Social Network Analysis (SNA) is the use of mathematical tools such as graph theory and linear algebra to mathematically analyze social networks.

SNA is a scientific approach to the study of structures of mutual relationships between entities. The variety of entities may include: people, organizations, geographies and countries. This method is widely applied in research for characterizing analysis and understanding phenomena in many areas. Despite the vast differences between entities and domains, there are characteristics and phenomena that are common to all networks. These characteristics, which will be discussed in the course, are largely explained by the network structure. The purpose of this course is to explore the main principles of social network theory and discuss research and applications on the field of SNA. During the course, mathematical tools for social network analysis will be studied mainly from graph theory.

SNA has become a widely applied method in research and business for inquiring the web of relationships on the individual, organizational and societal level. Therefore, in this course, students learn how to conduct SNA projects and how to approach SNA with theoretic, methodological, and computational rigor.

This course addresses several key areas:

• Introduction to social network theory.

• Algorithmic Network Theory - Game theory applications and algorithms in networks

• Key tools for analyzing social networks and centrality measures:

Degree centrality, Network density, Freeman centralization, Closeness centrality, Betweenness centrality, Eigenvector centrality.

• PageRank algorithms and link analysis algorithms (HITS algorithm).

• Influencer Marketing and Engagement Rate Calculation

• Network visualization and use of network analysis software to visualize networks (NodeXL שמג Gephi).

• Network effect and Diffusion in social networks.

• Review research and applications on social networks, and the impact of social networks on organizations and companies.

Abstract:

Course name: Mathematical Analysis Of Networks

Course code: 10358

Lecturer and director of the course: Dr. Michael Mann

This course introduces exponential random graph models (ERGMs), a powerful tool for modeling network data. ERGMs are a type of statistical model that can be used to describe the structure of a network, such as the distribution of edges, the number of triangles, or the degree distribution.

This course explores the foundations of creating probabilistic statistical models of networks. This is a big departure from the descriptive analysis of networks (eg measuring the centrality of a node) and also a fairly big departure from the statistical modeling of non-network data with the regression framework. Our goal for the course will be the development of statistical models that can accomplish the same general objectives as regression models (fitting parameters to data with probabilistic models), while accounting for the substantial endogenous complexity that is inherent to network data.

During the course we will explore primarily the exponential random graph model (ERGM), but alternative techniques such as the stochastic actor-based model (i.e. Sienna) will be considered as well.

At the beginning of the course we will deal with the application of mathematical tools for network analysis. In the first step, we will mathematically apply the description of the networks by adjacency matrix and demonstrate the algorithms for calculating the centrality measures in the adjacency matrix.

We will also deal with with mathematical applications in algorithms for finding cliques in networks or in Pagerank Algorithm (Eigenvector cenrality, Perron–Frobenius theorem and its applications in PageRank, Damping Factor) and we will also explore the alternative algorithm (HITS algorithm).