4.1 network analysis basic

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4.1 network analysis basic

  1. 1. Network analysis basic
  2. 2. • in-degree: how many directed edges (arcs)are incident on a node• out-degree: how may directed edgesoriginate at a node• Degree sequence: [4, 4, 3, 7, …]Node properties
  3. 3. Generated properties of node• Clustering coefficient: how your neighborsconnected together• ego-density: density of the surrounding netUCINET: Network>Ego-networks>egonet basic measures
  4. 4. • Directed or undirected• Weight, ranking, ...• Type, negative or positive, ...• Assigned-properties depending oncalculating network itself, e.g., betweennessEdge properties
  5. 5. Network Properties• Degree distribution: Frequency of degreesequences• Size: number of nodes (n)• Density: real relations divided by the maximumpossible relations• Diameter: the length of the longest path• Average degree of separation:Average length of allpossible shorted pathUCINET: Network>Cohesion>Density
  6. 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
  7. 7. Resolved by co-occurrence-ship
  8. 8. Network analysis basic
  9. 9. • DegreeHow many resource do you have?• ClosenessHow far apart are you from others?• BetweennessHow important are you for bridgingsub-communities?• CentralizationHow balanced are actors’ centrality?CentralityIndividuallevelGloballevel
  10. 10. • DensityHow does the network tied together?• Separation, DiameterHow far apart are you and your friends?• Cluster CoefficientHow do your neighbors be connected?IndividuallevelGloballevel
  11. 11. Visualization through analysis process1. Take a look2. Analyze and find significant features such as sub-components or special positions3. Draw the network according to the result ofanalysis4. Color by the node features (e.g., sex, position, ...)and create hypothesis5. Verify the hypothesis
  12. 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. 13. • Data is recorded with a clear natural-occurringboundary and nodes in a boundary form a finiteset.• What should be a possible boundary?‣ A fixed location or room, specified time or day, a finite contacttracing, a formal group in an organization, a family.‣ The boundary is known or decided firstly, a priori, to be anetwork.Policy of recording data
  14. 14. • No sampling and tend to include all of the actorsin some population(s).• Because network methods focus on relationsamong actors, actors cannot be sampledindependently to be included as observations.Policy of recording data (2)
  15. 15. • positivity A Priorimetaphysics-• -• --Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.
  16. 16. • Closed Complete- finiteset-• Singularity-• Consistency-Butts, Carter T. "Revisiting the foundations of network analysis." Science325.5939 (2009): 414-416.
  17. 17. • Different relation sampling policy will causedifferent results—Threshold effects on networkproperties• ThresholdThreshold• Threshold 0ConnectednessBetweenness• Threshold BetweennessDegree Betweenness• facebook10Application
  18. 18. • Full network data is necessary to properly define and measuremany 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 untilno new actors are identified, or until we decide to stop.- Useful to track down “special” population such as business contact networks, communityelites, deviant sub-cultures, avid stamp collectors, and kinship networks.- The snowball method may tend to overstate the "connectedness" and "solidarity" ofpopulations 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
  19. 19. Visualization
  20. 20. X Crossed-edgesX Uninformed-edgelengthX Overlappednodes and edges
  21. 21. A B C D E F G H I JA 0 1 1 1 0 1 0 0 0 0B 1 0 0 1 1 0 1 0 0 0C 1 0 0 1 0 1 0 0 0 0D 1 1 1 0 1 1 1 0 0 0E 0 1 0 1 0 0 1 0 0 0F 1 0 1 1 0 0 1 1 0 0G 0 1 0 1 1 1 0 1 0 0H 0 0 0 0 0 1 1 0 1 0I 0 0 0 0 0 0 0 1 0 1J 0 0 0 0 0 0 0 0 1 0Adjacent matrixdegree of BSymmetricM(1,4)=1, M(1,5)=0
  22. 22. Homans(1951) Metrics representation and manipulationA B C D E F G HA 1 1 1 1 1B 1 1 1C 1 1 1 1D 1 1 1E 1 1 1F 1 1 1G 1 1 1H 1 1 1 1D E C H A B F GD 1 1 1E 1 1 1C 1 1 1 1H 1 1 1 1A 1 1 1 1 1B 1 1 1F 1 1 1G 1 1 1

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