TELECOM 2000 Midterm Review Notes (Part 1)

TELECOM 2000 Midterm Review Notes (Part 1).md

Bridging, Brokerage, Closure, and the Strength of Weak Ties

Components

1. Connected component: A set of nodes that can all be reached from each other via a path
2. Largest connected component: The biggest
3. Giant component: A CC that comprises a significant fraction of the nodes in the network

Bridges

1. Bridge: A link that, if deleted, would put the two nodes in different components
2. Local bridge: A link that, if deleted, would put the connected nodes in much more distant parts of the network
   • Span of a local bridge: The length of the geodesic between the two nodes once the bridge is removed
3. Strong ties vs. weak ties
   • When we try to get or spread information, weak ties are more important than strong ones
   • Strong ties are with people similar to us, who have similar information
   • Homophily: we tend to know people who are similar to us on one or more dimensions
     • It can lead to difficulty in sorting cause and effect in social situations (Link -> Behavior or Behavior -> Link)
     • It also affects the spread of ideas and opinion formation by creating an echo chamber
4. Bridges and local bridges tend to be weaker than non-bridging links
   • Triadic closure: Two people with a common friend are more likely to become friends themselves
5. Embeddedness of an edge: The number of common neighbors shared by the two endpoints
   • All bridging links have embeddedness of 0

Closure, Brokerage, and Social Capital

1. Social capital: The benefit that an individual gains from their position in the social network
2. People who have many embedded links and high clustering gain social capital from closure
   • Advantages
     • Breed trust
     • Interactions along non-embedded links are riskier
     • Non-embedded links may mean more than one set of social norms
3. People whose links have low embeddedness are said to bridge structural holes
   • Advantages
     • Have better access to information
     • Gatekeepers between different communities
     • Face less competition from fundamentally similar neighbors
   • People who bridge structural holes gain social capital from brokerage

Network Measure: Centrality and Prestige

Centrality

1. Degree centrality: When the person with the most connections is most important
   
    
2. Closeness centrality (Distance centrality): When the person in the middle of the action is most central
   
    
   • Person with the highest closeness centrality has the shortest average distance to other nodes
3. Betweenness centrality: The most important people are those you have to go through to get to others
   
    
   • is the total number of geodesics between j and k

Centralization

1. Centralization: A measure of how centrality is distributed in the network
   
    
2. It tells us about how influence is spread across the network
   • High centralization: One node dominates the network
   • Low centralization: Trades are more evenly distributed

Prestige

1. Prestige: Centrality in directed networks
2. Measure:
   • Directed in-degree
     
      
   • Influence range: What fraction of the nodes in the network can reach you via directed paths

Models of Social Networks