introduction to social network analysis lluís coromina departament d’economia. universitat de...
TRANSCRIPT
Social network analysis is:
• a set of relational methods for systematically understanding and identifying connections among actors
Introduction
• Actors (nodes, points, vertices): - Individuals, Organizations, Events …
• Relations (lines, arcs, edges, ties): between pairs of actors.- Undirected (symmetric) / Directed (asymmetric)- Binary / Valued
Basic conceptsNetwork Components
1) Egocentered Networks• Data on a respondent (ego) and the people they are connected to.
Measures:SizeTypes of relations
Basic concepts
Types of network data:
2) Complete Networks
• Connections among all members of a population.
• Data on all actors within a particular (relevant) boundary.
• Never exactly complete (due to missing data), but boundaries are set
• Ex: Friendships among workers in a company.
Measures:Graph properties DensitySub-groupsPositions
Background
Types of network data:
The unit of interest in a network are the combined sets of actors and their relations.
We represent actors with points and relations with lines.
Example:
Social Network data
a
b
c e
d
In general, a relation can be:Undirected / DirectedBinary / Valued
a
b
c e
d
Undirected, binary Directed, binary
a
b
c e
d
a
b
c e
d
Undirected, Valued Directed, Valued
a
b
c e
d1 3
4
21
Social Network data
From pictures to matrices
Undirected, binary Directed, binary
a b c d ea
b
c
d
e
1
1
1 1 1
1 1
a b c d ea
b
c
d
e
1
1 1
1 1 1
1 11 1
Basic Data Structures
Social Network data
a
b
c e
d
a
b
c e
d
d e
c
Indirect connections are what make networks systems. One actor can reach another if there is a path in the graph connecting them.
a
b
c e
d
f
b f
a
Connectivity
Measuring Networks
Distance is measured by the (weighted) number of relations separating a pair, Using the shortest path.
Actor “a” is: 1 step from 4 2 steps from 5 3 steps from 4 4 steps from 3 5 steps from 1
Distance & number of paths
Measuring Networks
a
An information network:
Email exchanges within the Reagan white house, early 1980s(source: Blanton, 1995)
Measuring Networks
Centrality refers to (one dimension of) location, identifying where an actor resides in a network.
Centrality
Measuring Networks
Centrality is fairly straight forward: we want to identify which nodes are in the ‘center’ of the network. In the sense that they have many and important connections.
Three standard centrality measures capture a wide range of “importance” in a network:
DegreeClosenessBetweenness
The most intuitive notion of centrality focuses on degree. Degree is the number of lines, and the actor with the most lines is the most important:
Centrality
Measuring Networks
Centrality
Measuring Networks
Relative measure of Degree Centrality:
1
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ppaPC
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ikD
Degree Centrality:
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ki
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ikD ppaPC
A second measure is closeness centrality. An actor is considered important if he/she is relatively close to all other actors.
Closeness is based on the inverse of the distance of each actor to every other actor in the network.
Closeness Centrality:
Relative Closeness Centrality
Centrality
Measuring Networks
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Closeness Centrality
Centrality
Measuring Networks
Betweenness Centrality:Model based on communication flow: A person who lies on
communication paths can control communication flow, and is thus important. Betweenness centrality counts the number of shortest paths between i and k that actor j resides on.
b
a
C d e f g h
Centrality
Measuring Networks
Centrality
Measuring Networks
Betweenness centrality can be defined in terms of probability (1/gij),
CB(pk) = iij(pk) = =
gij = number of geodesics that bond actors pi and pj.gij(pk)= number of geodesics which bond pi and pj and content pk.iij(pk) = probability that actor pk is in a geodesic randomly chosen among the ones which join pi and pj.
Betweenness centrality is the sum of these probabilities (Freeman, 1979).
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1
ijkij pg
ij
kij
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Normalizad: C’B(pk) = CB(pk) / [(n-1)(n-2)/2]
Betweenness Centrality:
Centrality
Measuring Networks
If we want to measure the degree to which the graph as a whole is centralized, we look at the dispersion of centrality:
Freeman’s general formula for centralization (which ranges from 0 to 1):
)]2)(1[(
)()(1
*
nn
pCpCC
n
i iDDD
Centralization
Measuring Networks
Degree Centralization Scores
Freeman: 1.0 Freeman: .02 Freeman: 0.0
Centralization
Measuring Networks
Density
Measuring Networks
The more actors are connected to one another, the more dense the network will be. Undirected network: n(n-1)/2 = 2n-1 possible pairs of actors.
Δ =
Directed network: n(n-1)*2/2 = 2n-2possible lines.
ΔD =
2/)1( nn
L
)1( nn
L
Freeman: .25 Freeman: .23 Freeman: 0.25
Density
Measuring Networks
UCINET•The Standard network analysis program, runs in Windows•Good for computing measures of network topography for single nets•Input-Output of data is a special 2-file format, but is now able to read PAJEK files directly. •Not optimal for large networks•Available from:
Analytic Technologies
Social Network Software
PAJEK •Program for analyzing and plotting very large networks•Intuitive windows interface•Started mainly a graphics program, but has expanded to a wide range of analytic capabilities•Can link to the R statistical package•Free•Available from: http://vlado.fmf.uni-lj.si/pub/networks/pajek/
Social Network Software
NetDraw•Also very new, but by one of the best known names in network analysis software. •Free
Social Network Software