🕸️Networked Life Unit 10 – Social Network Analysis

What's Social Network Analysis?

• Social Network Analysis (SNA) studies the relationships and interactions between individuals, groups, or entities within a network
• Focuses on understanding the patterns, structures, and dynamics of social networks
• Analyzes how the structure of a network influences the behavior and outcomes of its members
• Combines concepts from graph theory, sociology, and computer science to examine social phenomena
• Helps identify influential actors, detect communities, and understand information flow within a network
• Enables researchers to visualize and quantify complex social relationships using mathematical and computational tools
• Provides insights into various domains such as social media, organizational behavior, and disease transmission

Key Concepts and Terminology

• Nodes (vertices) represent individual actors or entities within a network (people, organizations, or web pages)
• Edges (links or ties) depict the relationships or interactions between nodes (friendships, communication, or hyperlinks)
• Directed edges have a specific direction indicating the flow of information or influence from one node to another
• Undirected edges represent mutual or bidirectional relationships between nodes
• Degree refers to the number of edges connected to a node
  • In-degree counts the number of incoming edges to a node
  • Out-degree counts the number of outgoing edges from a node
• Weighted edges assign a value to the strength or intensity of the relationship between nodes
• Adjacency matrix is a square matrix representing the connections between nodes in a network
• Centrality measures quantify the importance or influence of nodes based on their position in the network

Network Structures and Properties

• Network density measures the proportion of actual connections relative to the total possible connections in a network
• Clustering coefficient quantifies the tendency of nodes to form tightly connected groups or clusters
• Average path length calculates the average number of steps required to traverse between any two nodes in the network
• Diameter represents the longest shortest path between any two nodes in the network
• Degree distribution describes the probability distribution of node degrees in a network
  • Scale-free networks exhibit a power-law degree distribution, with a few high-degree nodes and many low-degree nodes
  • Random networks follow a Poisson degree distribution, with most nodes having a similar number of connections
• Assortativity measures the tendency of nodes with similar attributes or degrees to connect with each other
• Modularity quantifies the strength of division of a network into distinct communities or modules

Data Collection and Visualization

• Data collection involves gathering information about the nodes and edges in a social network
• Surveys and questionnaires can be used to collect self-reported data on social relationships and interactions
• Digital trace data, such as email logs, phone records, or social media interactions, provide a wealth of network data
• Web scraping techniques extract network data from online sources, such as hyperlinks between websites
• Network visualization tools, like Gephi or Cytoscape, enable the visual representation of social networks
  • Force-directed layouts position nodes based on the strength of their connections, revealing network structure
  • Color-coding and sizing of nodes and edges can represent various attributes or centrality measures
• Interactive visualizations allow users to explore and analyze social networks dynamically

Centrality Measures

• Centrality measures identify the most important or influential nodes in a network based on their structural position
• Degree centrality considers nodes with a high number of connections as more central and influential
• Closeness centrality measures how quickly a node can reach all other nodes in the network
  • Nodes with high closeness centrality have short average path lengths to other nodes
• Betweenness centrality quantifies the extent to which a node lies on the shortest paths between other node pairs
  • Nodes with high betweenness centrality act as bridges or gatekeepers, controlling information flow
• Eigenvector centrality assigns higher importance to nodes connected to other highly connected nodes
  • PageRank, used by Google, is a variant of eigenvector centrality for ranking web pages
• Katz centrality extends eigenvector centrality by considering both direct and indirect connections
• Centralization measures the extent to which a network is dominated by a few highly central nodes

Community Detection

• Community detection aims to identify densely connected groups of nodes within a network
• Communities (clusters or modules) are subsets of nodes with more connections among themselves than with nodes outside the community
• Modularity optimization is a popular approach for community detection, maximizing the difference between observed and expected connections within communities
  • Louvain algorithm is a fast and efficient method for modularity optimization
• Hierarchical clustering methods, such as Girvan-Newman algorithm, iteratively remove edges to reveal a hierarchy of communities
• Stochastic block models assume that nodes belong to latent communities and aim to infer the underlying community structure
• Label propagation algorithms assign community labels to nodes and iteratively update them based on the labels of neighboring nodes
• Overlapping community detection allows nodes to belong to multiple communities simultaneously
• Evaluation of community detection results can be done using ground truth data or internal quality measures like modularity or conductance

Network Dynamics and Diffusion

• Network dynamics studies how networks evolve and change over time
• Preferential attachment is a mechanism for network growth where new nodes preferentially connect to existing high-degree nodes
  • Barabási-Albert model generates scale-free networks using preferential attachment
• Small-world networks exhibit high clustering and low average path lengths, enabling efficient information diffusion
  • Watts-Strogatz model generates small-world networks by rewiring edges in a regular lattice
• Diffusion processes, such as information cascades or disease spread, propagate through networks
• Susceptible-Infected-Recovered (SIR) model simulates the spread of infectious diseases in a network
  • Nodes transition from susceptible to infected to recovered states based on contact with infected neighbors
• Threshold models describe the adoption of behaviors or innovations based on the proportion of adopting neighbors
• Opinion dynamics models, like the Voter model or DeGroot model, simulate the spread and convergence of opinions in a network
• Influence maximization identifies a set of initial nodes to maximize the spread of information or adoption in a network

Real-World Applications

• Social media analysis examines the structure and dynamics of online social networks (Twitter, Facebook)
• Recommendation systems leverage network data to suggest products, content, or connections to users
• Epidemiology uses network models to understand and predict the spread of infectious diseases
• Organizational network analysis studies the formal and informal relationships within organizations to optimize collaboration and performance
• Criminal network analysis identifies key actors and relationships in criminal organizations to disrupt illegal activities
• Marketing and viral marketing campaigns utilize network effects to promote products or ideas
• Political science analyzes the formation and influence of political networks, such as voting behavior or campaign donations
• Bioinformatics applies network analysis to study biological networks, such as protein-protein interactions or gene regulatory networks