![• in-degree: how many directed edges (arcs) are incident on a node • out-degree: how may directed edges originate at a node • Degree sequence: [4, 4, 3, 7, …] Node properties](https://image.slidesharecdn.com/4-1networkanalysisbasic-130425091629-phpapp02/75/4-1-network-analysis-basic-2-2048.jpg)
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4.1 network analysis basic
- Network analysis involves examining properties of nodes and edges in a network. Node properties include degree, clustering coefficient, and ego-density. Edge properties include weight and type. - Network properties examined at a global level include degree distribution, density, diameter, and average path length. Centrality measures like betweenness are also calculated. - There are different modes of networks including one-mode, two-mode, and affiliation networks. Levels of analysis include ego-network, partial network, and whole network analysis.
4.1 network analysis basic
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- 2. • in-degree: howmany directed edges (arcs) are incident on a node • out-degree: how may directed edges originate at a node • Degree sequence: [4, 4, 3, 7, …] Node properties
- 3. Generated properties ofnode • Clustering coefficient: how your neighbors connected together • ego-density: density of the surrounding net UCINET: Network>Ego-networks>egonet basic measures
- 4. • Directed orundirected • Weight, ranking, ... • Type, negative or positive, ... • Assigned-properties depending on calculating network itself, e.g., betweenness Edge properties
- 5. Network Properties • Degreedistribution: Frequency of degree sequences • Size: number of nodes (n) • Density: real relations divided by the maximum possible relations • Diameter: the length of the longest path • Average degree of separation:Average length of all possible shorted path UCINET: Network>Cohesion>Density
- 6. Mode of network •One-mode network ‣ Friendship ‣ Collaboration e.g., User-paper represented by 2-mode network • Two-mode network—bipartite network ‣ User-borrowed book, co-bought ‣ Affiliation network— e.g., Member-Guild, Employee-Company
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- 9. • Degree How manyresource do you have? • Closeness How far apart are you from others? • Betweenness How important are you for bridging sub-communities? • Centralization How balanced are actors’ centrality? Centrality Individual level Global level
- 10. • Density How doesthe network tied together? • Separation, Diameter How far apart are you and your friends? • Cluster Coefficient How do your neighbors be connected? Individual level Global level
- 11. Visualization through analysisprocess 1. Take a look 2. Analyze and find significant features such as sub- components or special positions 3. Draw the network according to the result of analysis 4. Color by the node features (e.g., sex, position, ...) and create hypothesis 5. Verify the hypothesis
- 12. • Ego-network Analysis - - •Partial Network Analysis - One, two or three steps network two steps network - Boundary or sub-cluster of network • Whole Network Analysis - / Motif - Levels of network analysis
- 13. • Data isrecorded with a clear natural-occurring boundary and nodes in a boundary form a finite set. • What should be a possible boundary? ‣ A fixed location or room, specified time or day, a finite contact tracing, a formal group in an organization, a family. ‣ The boundary is known or decided firstly, a priori, to be a network. Policy of recording data
- 14. • No samplingand tend to include all of the actors in some population(s). • Because network methods focus on relations among actors, actors cannot be sampled independently to be included as observations. Policy of recording data (2)
- 15. • positivity APriori metaphysics - • - • - - Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.
- 16. • Closed Complete -finite set - • Singularity - • Consistency - Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.
- 17. • Different relationsampling policy will cause different results—Threshold effects on network properties • Threshold Threshold • Threshold 0 Connectedness Betweenness • Threshold Betweenness Degree Betweenness • facebook 10 Application
- 18. • Full networkdata is necessary to properly define and measure many of the structural concepts of network analysis (e.g. between-ness), however, very expensive. • Snowball methods begin with a focal actor or set of actors until no new actors are identified, or until we decide to stop. - Useful to track down “special” population such as business contact networks, community elites, deviant sub-cultures, avid stamp collectors, and kinship networks. - The snowball method may tend to overstate the "connectedness" and "solidarity" of populations of actors. - There is no guaranteed way of finding all of the connected individuals in the population. - How to select the first node (initial problem of sampling)? - Incomplete problem of the snowball methods can be solved by use of multiple initial nodes. Methods of sampling ties
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- 20. X Crossed-edges X Uninformed-edge length XOverlapped nodes and edges
- 24. A B CD E F G H I J A 0 1 1 1 0 1 0 0 0 0 B 1 0 0 1 1 0 1 0 0 0 C 1 0 0 1 0 1 0 0 0 0 D 1 1 1 0 1 1 1 0 0 0 E 0 1 0 1 0 0 1 0 0 0 F 1 0 1 1 0 0 1 1 0 0 G 0 1 0 1 1 1 0 1 0 0 H 0 0 0 0 0 1 1 0 1 0 I 0 0 0 0 0 0 0 1 0 1 J 0 0 0 0 0 0 0 0 1 0 Adjacent matrix degree of B Symmetric M(1,4)=1, M(1,5)=0
- 25. Homans(1951) Metrics representationand manipulation A B C D E F G H A 1 1 1 1 1 B 1 1 1 C 1 1 1 1 D 1 1 1 E 1 1 1 F 1 1 1 G 1 1 1 H 1 1 1 1 D E C H A B F G D 1 1 1 E 1 1 1 C 1 1 1 1 H 1 1 1 1 A 1 1 1 1 1 B 1 1 1 F 1 1 1 G 1 1 1