This module covers Community Structure in networks: the organization of nodes in a network into clusters or communities, where nodes within the same community have a higher density of connections within their community than across other communities. We explore algorithms to identify communities in networks and evaluate them. Key topics include Modularity, a measure that quantifies the strength of the division of a network into modules or communities; the Girvan-Newman algorithm, a method that systematically removes edges from the network to find the best division based on edge betweenness centrality; Agglomerative Hierarchical Clustering, a technique that builds a hierarchy of clusters by progressively merging groups based on their distance or similarity; and Label Propagation, an algorithm for detecting communities based on spreading labels throughout the network and forming communities based on the dominant label. We also discuss applications to the community detection problem in real-world scenarios.

This module expands on network generative models, building on previously covered models such as Small-World and Preferential Attachment models. We'll explore the Erdős-Rényi model, which connects nodes randomly and serves as a baseline for understanding random graph theory. The module also covers the Stochastic Block Model, which is useful for modeling community structures by grouping nodes and connecting them based on group membership. Additionally, we explore the Configuration Model, which is used for creating random networks that maintain a given degree distribution.

This module explores how ideas, diseases, and information spread in networks using models like SI, SIS, SIR, Independent Cascade, and Linear Threshold. Learners will simulate these models with Python, modify them, and tackle the influence maximization problem, identifying key nodes to optimize information or behavior spread.