Introduction to Social Network Analysis

• Interdependence among actors and their actions
• Relationships between actors allow resource flows
• Network structure offers individuals opportunities & constraints
• Structure emerges from patterned relationships between actors

1. Intuition of social structure as ties bonding social actors
2. Informed by systematic empirical data
3. Visualization plays a substantial role
4. Requires mathematical and/or computational models

1. Prehistory
2. Birth
1. Moreno & Sociometry (1930s)
2. Harvard
3. Dark Ages (1940s-1960s)
4. Harvard Renaissance
5. Organizational integration

• Network science
• Social media
• Big data

• Vertex
• Node

• Edges
• Arcs

• Directed undirected?
• Weighted or unweighted?
• Nominal, ordinal, interval, or ratio scale?
• Signed or unsigned?
• Loops?
• Time sensitivity?
• Static
• Moving window
• Real-time
• Accumulation and decay

• Simple graph
  

• Simple graph
• Multigraph

• Simple graph
  
• Multigraph
• Hypergraph

• Simple graph
• Multigraph
• Hypergraph
• Directed Acyclic Graph

• Simple graph
• Multigraph
• Hypergraph
• Directed acyclic graph
• Two-Mode Network

• Simple graph
• Multigraph
• Hypergraph
• Directed acyclic graph
• Two-mode network
• Ego Networks

• Matrix

• Matrix
• Edgelist

• Matrix
• Edgelist
• Set Notation

ℕ = {n1,n2,n3,n4,n5}
𝕃 = {l1,l2,l3,l4}

l1 = (n1,n3)
l2 = (n1,n5)

l3 = (n2,n4)


l4 = (n3,n5)


𝔾 = (ℕ,𝕃)

• Matrix
• Edgelist
• Set notation
• Sociogram

• Brokerage
  
• Characterized by only two ties among three actors
• Transitivity, "clustering," triadic closure
• Your friends are often friends with each other
• Typically measured by weak criterion
• (3*Triangles) / (Connected Triples)

• Brokerage
• i → j → k, i ↛ k, k ↛ i 
• Transitivity
• Weak (most common)
• i → j → k, if i → k
  
• Strong 
• i → j → k, iff i → k
  
• Cycles
• i → j → k → i
  

Path

• Land masses are nodes, bridges are edges
  
• Would need zero or two nodes of odd degree

Shortest path between two nodes

Length of the shortest path between two nodes

1. Degree
2. Betweenness
3. Closeness
4. Eigenvector

• Cumulative Advantage
  
• Matthew Effect (Merton)
  

• Friendship Paradox (Feld 1991)
  

• Centrality accumulates from the centralities of associated alters
• Favors large, dense subgraphs (cliques)
• Equal to the first eigenvector of the network's adjacency matrix

• Interact relatively frequently
• Have strong, direct ties within themselves
• Display high internal density
• Share attitudes and behaviors within themselves
• Exert pressure and social norms internally

• Geodesic-based approaches
• n-cliques, n-clans, n-clubs
• Not robust to edge deletion
• No in-group/out-group distinction
  
• Degree-based approaches
• k-plexes, k-cores
• No ingroup/outgroup distinction
• Connectivity-based approaches
• Lambda sets, Moody & White's (2003) cohesive blocks
• Nodes not necessarily directly or closely connected
• Ingroup/outgroup distinctions
• LS Sets
• Modularity-based methods

• Ties going inward
• Ties going outward
• Total ties

• Hierarchical Algorithms
• Top-Down
• Girvan-Newman (Newman & Girvan 2004)
• Leading Eigenvector* (Newman 2006)
• Bottom-Up
• Fast-Greedy* (Clauset et al. 2004)
• Walktrap (Pons & Latapy 2005)
• Louvain method*, ** (Blondel et al. 2008)
• Spin-Glass (Reichardt & Bornholdt 2006; Traag & Bruggeman 2008)

1. Generalized
2. Differential (some groups more homophilous than others)
3. Matching (some groups prefer other groups in addition to themselves)

1. Population effects
2. Degree correlated attributes
3. Triadic closure
   

1. An artifact
2. A sender
3. A receiver
4. A channel

• Account for homophily
• Theorizing channels and artifacts
• Conceptualizing time
• Adoption rate
• Decay
• Inhibitors

• Preferential attachment
• Homophily / assortativity
• Block models
  
• Small world
• Network evolution models
  
• p* / ERGM family

1. Discrete subsets of actors into "positions"
2. Relationships within and between positions

1. Relationship between positions and attributes
2. Structure of relationships

1. High clustering
2. Short path lengths

• Growing models
• Nodes & links added until N nodes reached
• Dynamical models
• Adding & removing nodes until equilibrium reached