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Lecture 6

Lecture 6 Oct 19 Lecture.docx

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Alexandra Marin

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
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