false

Class Notes
(838,541)

Canada
(510,933)

University of Toronto St. George
(44,098)

Sociology
(3,264)

SOC355H1
(33)

Alexandra Marin
(33)

Lecture 6

by
OneClass3158

Unlock Document

Sociology

SOC355H1

Alexandra Marin

Fall

Description

SOC355Y1
Lecture: October 19, 2010
Last week you learned:
- To collect network data, first pick your nodes and then pick your relations
and then think about your measures
- Sampling from networks is harder than it looks
- There are lots of ways of collecting network data: They all have advantages
but none of them are perfect
- Measures of connectivity (Geodesics, Isolates, Degree, Neighbourhood,
Density)
Today’s Outline
- Density again
- Centrality and centralization
- Subgroups
o Components
o Cliques
- Geodesic – undefined if nodes are not connected
- Isolates
- Degree: number of connections a node has, kind of centrality
- Neighbourhood- type of nodes connected to an ego node
- Density- second most important
- Size- first important
Density is a proportion of the number of ties that exist in a network over the
number that could exist (Fraction)
# of ties that exist
# of ties that could exist
- Goes from 0-1 because it is a proportion
- L /
- Numerator Undirected: count lines
- Numerator: Directed network: count arrow heads
- Denominator: Undirected (only one line between two nodes, therefore divide
by 2 to get rid of half) n -n/2
2
- Denominator: Directed n -n
- Express density up to three decimal places (for problem set) Centrality- a property of a node, not a whole network, so every node will have its
own centrality
- When we want to measure something, we must first define what we mean by
it – therefore define centrality
- Centrality- to deal with the definition let’s look at what looks central and
what properties are included
- Centrality: high degree, connected to other nodes with a high degree…
- It may be hard to find central nodes with complex networks
- Freeman argued a lot about centrality- he argued if we really want to learn
what we mean by centrality, we should think about a case where it is
completely unambiguous, no one can argue what the most central node is.
He looked at the star network:
3 things freeman came up with about the central node
A – The central node – the three advantages of being A – and developed 3 measures
of centrality
1. Has a high degree of activity
2. Could easily reach every other node and be reached by every other node
3. Control, control of the other nodes
B
E A C
D
- What centrality is about… #1 if you are worried about the high degree of
activity you would use degree centrality (the number of connections a node
has) – for A it would be 4, the degree centrality for every other node but A is
1. If you have a directed network you have indegree centrality (number of
connections that come into a node) and outdegree centrality (the number of
connections the node sends out) – this captures how much activity is in the
network
- #2: If concerned about the second being could easily reach every other node
-REACH – closeness centrality is about how far is it to other nodes- (do not
worry about calculating just know counting degree centrality) takes
geodesics and figures out how far each one is, then take the inverse
(closeness centrality) - #3: If you think the important thing is control then you will be interested in
“Betweeness centrality”- a measure of the extent to which a node lies on the
geodesics between other pairs of nodes and then weights on how long there
are or how many other nodes on the geodesic – ideally you want to be the
only node on a geodesics to boost centrality
3 measures of centrality (listed above)
We can also think about how networks differ in terms of centralization (not
a measure of each node but a measure of the network as a whole, the
measure to which a network is dominated by a single node)
- High between centrality – A is high between centrality, degree is not as high
A
- Degree centrality is the same as local centrality – the number of nodes a
node is connected to
- Bonacich or power centrality– came up with another measure of centrality
based on the idea that it is different to be A then B – takes into account the
degree of the node connected to- it is different- this kind of centrality –
determining if it is better
- - B is better to be if you want information! But if you are selling something it
is better to be A (because you are selling things

More
Less
Related notes for SOC355H1

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.