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Social Network Analysis
Weak ties, networks, etc
67
Management
Undergraduate 4
04/25/2010

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Term
Actors
Definition
nodes, verticies
Term
Relations
Definition
links, ties, edges
Term
Network
Definition
set of nodes and collection of links between these nodes
Term
Component
Definition
Connected subset of network nodes and links
Term
Triad
Definition
group of three nodes
Term
dyad
Definition
group of two nodes
Term
pendant
Definition
an actor with one tie connected to a group
Term
isolate
Definition
node with no ties
Term
Sociomatrix
Definition
matrix showing the relationships between nodes (directed=non symmetric)
Term
one vs two mode graphs
Definition
Actor-actor & actor-event- bipartite sociomatrix
Term
Degree Centrality
Definition
Total number of links of a node- "popularity" in degree vs outdegree
Term
Closeness centrality
Definition
How easily one actor can reach rest of network
•Actor with shortest average path length
•“Pulse-taker
Term
Betweenness Centrality
Definition
How much an actor lies between distinct groups
•Number of geodesics passing through actor
•“Broker”
Term
Eigenvector Centrality
Definition
A node’s centrality is a function of its neighbors’ centralities
Highest between and\or degree central actor often highest eigenvaluecentral actor, but not always the case with less central actors
Term
star
Definition
actor highly central to network
Term
liason
Definition
actor with unique links to two or more groups, but a member of neither
Term
bridge
Definition
actor who is a member of two or more groups
Term
gatekeeper
Definition
actor who is the sole link from one part of the network to another
-Insider brokering outsiders' access to group
Term
coordinator
Definition
broker within group
Term
consultant
Definition
outsider brokering between insiders
Term
representative
Definition
insider brokering insiders' access to outsiders
Term
Social Capital
Definition
Network of trusted contacts in diverse social worlds
Term
Private info
Definition
given by trust in networks, Trust is first characteristic of Paul Revere network
Term
Diversity
Definition
Second paul revere network characteristic,
It helps you transcend your natural limitations
Term
Pyramid corporation
Definition
old, Formal power
- Directives, standard procedures
Term
pancake corporation
Definition
new, Networks
- Rainmakers, opinion leaders, connectors
Term
Brokerage
Definition
3rd characteristic of PRevere network, It connects separate clusters of knowledge quickly and efficiently
Term
Paul Revere Networks
Definition
Trust = Private Information
(Suspicion will save you 1 gold coin, but trust will earn you 2)

High Diversity
Low redundancy
High Brokerage
Diversity = Skills
(Diversity “squares” your value in a network)
Brokerage = Power
(6 Degrees of Separation is key)
Term
power law distributions
Definition
80-20, scale-free,
Term
path length
Definition
number of links
between two nodes (degrees of
separa2on)
Term
Geodesic
Definition
Shortest path length
between two nodes
Term
eccentricity
Definition
Each actor’s longest
geodesic
Term
Diameter
Definition
Network’s largest
geodesic\eccentricity
Term
shortcut
Definition
paths that bypass
clusters
Term
density
Definition
Observed edges in network / maximum possible edges
Term
clustering
Definition
Count 2es among alters, removing ego and 2es to ego
• Observed 2es in actor’s ego network / maximum possible
2es in ego network
Term
network centralization
Definition
Varia2on in individual actors’ centrali2es
• High centraliza2on when few actors possess higher
centrality than average
• Low centraliza2on when actors all have similar
centrali2es
Term
Small worlds
Definition
Paradox: Individuals within the
network are highly clustered but
also have small average geodesics
to other members
• Randomly rewiring a frac2on of
links on a regularly‐clustered
network dras2cally shortens
average eccentricity
• Random rewiring, however
s2ll maintains high clustering
over several orders of
magnitude
Term
n-step ego network
Definition
network of
all actors and their shared 2es, N
steps away from ego
Term
connected component
Definition
Every actor is reachable from
every other actor
Term
giant component
Definition
Largest connected component
Term
subgraph
Definition
Subsets of actors that are
disconnected from each other
Term
clique
Definition
Subset of maximally‐connected
actors
Term
reciprocity, transitivity, closure
Definition
transitivity- A>B & B>C =A>C
closure two two-way relationships in group of three being completed by third two-way relationship
Term
structural holes
Definition
Places where people are unconnected in a network
Term
Brokers
Definition
Actors who exploit structural holes
• Gain access to informa2on, power to filter, 2ming
for compe22ve
Term
Structural Equivalence
Definition
One actor having the same set of relations as another actor (siblings)
Term
automorphic equivalence
Definition
sets having same patterns of ties and are completely substitutable (cousins)
Term
regular equivalence
Definition
One actor occupying a similar posi2on as
another actor (division managers)
Term
Closure
Definition
Process of genera2ng highly equivalent posi2ons
• Greater trust,
high reciprocity and exchange
• Increasing redundancy,
greater constraint
Term
Cartwright-HararyTheorem
Definition
If a graph is balanced, then either
•All pairs of nodes are friends
•There exist groups that are friendly within the group but members of groups are antagonistic to other groups
Term
bottom up approach
Definition
Cliques, clans, plexes, & cores
Term
top down approach
Definition
Weak & strong components, blocks & cutpoints, lambda sets & bridges
Term
Clique
Definition
Largest subset of actors that are directly and completely connected to the rest of the set
Term
N-Cliques
Definition
long and stringy
Largest subset of actors that are completely-connected with rest of the set within N steps
-possibly connected by non members
Term
N-Clans
Definition
Path between any two members of an N-clique must occur via members of the N-clique
Term
k-plex
Definition
Node is a member of a “clique” of size N if it has direct ties to N-K members of that “clique”
-create lots of sub groups
Term
K-core
Definition
- more relaxed than k-plex
-Maximal group of actors all connected to K other members of the group
•Connection rather than immersion, closure, or clustering
Term
F-group
Definition
max group made by strong/weakly (valued) transitive triads
Term
cutpoint
Definition
Removing a node creates a new component
•Resulting divisions are blocks
Term
bridges
Definition
Removing a link creates a new component
Term
Lambda sets
Definition
Importance of relationships based on flux through link
•“Betweenness centrality” for a link
Term
homophily
Definition
tendency of actors to bond with those that are similar to themselves
-status homophily vs value-homophily
Term
Watts and Strogatz model
Definition
based on homophily and weak ties
-random graph generator that produces graph with small world properties (clustering and low average geodesic)
-but homogenous in degree (not a scale-free network)
Term
Cognitive social networks
Definition
who they think you know
Term
cognitive knowledge networks
Definition
who you think knows what
Term
local gatekeeper
Definition
has ties to two people without ties to eachother
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