Social Network Based Information Systems Don Steiny University of Oulu, Finland
Class goals <ul><li>Become familiar with techniques for analyzing social networks </li></ul><ul><li>Learn some of the prob...
Today <ul><li>Get acquainted  </li></ul><ul><ul><li>I’ll really introduce myself </li></ul></ul><ul><ul><li>I will meet ea...
Papers <ul><li>The Strength of Weak Ties - Mark Granovetter </li></ul><ul><li>An Experimental Study of the Small Worlds Pr...
More Papers <ul><li>The Diffusion of an Innovation among Physicians - James Colman, Elihu Katz, Herbert Menzel </li></ul><...
Still more papers <ul><li>The Iron Cage Revisited: Institutional Isomorphism and Collective Rationality in Organizational ...
More papers yet <ul><li>From Community of Innovation to Community of Inertia - The Rise and Fall of the U.S. Tire Industry...
Whew, last of papers <ul><li>*What Creates Energy in Organizations - Rob Cross and Andrew Parker </li></ul><ul><li>World S...
Who Does What? <ul><li>Anthropologists – kinship relations, friendship gift giving </li></ul><ul><li>Social psychologists ...
Some terms <ul><li>A  graph  is a set of vertices and a set of lines between pairs of vertices. </li></ul><ul><li>A  verte...
Our personal networks <ul><li>4 work sheets </li></ul><ul><li>Draw the network </li></ul><ul><li>Discussion </li></ul>
Dining Table Partners
Pajek data files <ul><li>.net – network files </li></ul><ul><li>.clu – partition files </li></ul><ul><li>.vec – vector fil...
Pajek Data File <ul><li>*Vertices  26 </li></ul><ul><li>1 &quot;Ada&quot;  0.1646 0.1077 0.5000 </li></ul><ul><li>2 &quot;...
Pajek files <ul><li>Let’s find the file Dining-table_partners.net, take a look at it with notepad. </li></ul>
Pajek Main Screen
Convert arcs to edges
Report Screen
Dialogue Box Info->Network->General
Draw Screen
Draw Screen Experience <ul><li>Load the file “dining_table_partners.net” and go through the handout labeled “Draw Screen” ...
Networks as matrices – joke network
Matrix of joke network
Thinking about matrices <ul><li>How would the matrix be different if it was an undirected graph? </li></ul><ul><li>How wou...
Create Pajek file from joke network <ul><li>Translates graphs into a simple file format </li></ul><ul><li>Usually this is ...
Compare networks <ul><li>Generate random networks with the same number of nodes as the dining table partners network. </li...
SNA Measurements <ul><li>Prevalent SNA  measures  at the   </li></ul><ul><li>   Individual level:   centrality and   pres...
Partitions <ul><li>A partition of a networks is a classification or clustering of the vertices in the networks such that e...
World System <ul><li>Go through the “World System” example  </li></ul><ul><li>Open the trade network and energize the posi...
World System
Trade Within South America – local view
Trade between continents – global view
World System Positions in South America – global view
Contextual view
World System GDP Vector
Fun with partitions <ul><li>There are several partition exercises we will work on now. </li></ul>
File: Attiro.net <ul><li>Load Attiro.net </li></ul>
Visiting Ties in Attiro
Density and Degree <ul><li>Density is the number of lines in a simple network expressed as a proportion of the maximum num...
Degree measures <ul><li>Info>Network>General </li></ul><ul><li>Net>Transform>Arcs>Edges>All </li></ul><ul><li>File>Network...
Exercise – Compare Networks <ul><li>Compare the network SanJuanSur.net to the Attiro network.  Is this network more cohesi...
Ajacent, indegree, outdegree <ul><li>Two vertices are adjacent if they are connected by a line. </li></ul><ul><li>The  ind...
Semiwalks and walks <ul><li>A  semiwalk  from vertex u to vertex v is a sequence of lines such that the end vertex of one ...
Paths and Semipaths <ul><li>A  semipath  is a semiwalk in which no vertex in between the first and last vertex of the semi...
Connection <ul><li>A network is (weakly)  connected  if each pair of vertices is connected by a semipath. </li></ul><ul><l...
Weak and Strong Components <ul><li>A (weak)  component  is a maximal (weakly) connected subnetworks. </li></ul><ul><li>A  ...
Find components: Attiro.net <ul><li>Net>Components>Strong (raise number to eliminate uninteresting components) </li></ul><...
Cores <ul><li>A  k-core  is a maximal subnetwork in which every vertex has at least degree  k  within the subnetwork. </li...
K-cores in Attiro visting network
Extracting k-cores <ul><li>Net>Partitions>Core>Input,Output,All </li></ul><ul><li>Operations>Extract from Network>Partitio...
Exercise: Extract k-cores <ul><li>Determine the k-cores in the network ExerciseII.net and extract the 4-core from the netw...
Cliques <ul><li>A clique is a maximal complete subnetwork containing 3 vertices or more. </li></ul>
Clique detection (Attiro.net) <ul><li>Net>Transform>Arcs>Edges>All </li></ul><ul><li>Nets>First Network,Second Network </l...
Signed Graph <ul><li>A signed graph is a graph in which eash line carries either a positive or a negative number. </li></ul>
Cycles, semicycles <ul><li>A cycle is a closed path. </li></ul><ul><li>A semicycle is a closed semipath. </li></ul><ul><li...
Eight possible triadic constellations
Determining the balance of a relationship
Tendency towards balance
Clustering <ul><li>A cycle or semicycle is clusterable if it does not contain exactly one negative arc. </li></ul><ul><li>...
Balance in the Monastery
Computing Balance <ul><li>[Draw]>Options>Values of Lines>Similarities </li></ul><ul><li>Partitions>Create Random Partition...
Three solutions with one error
Balance over time <ul><li>Groups tend towards balance over time </li></ul><ul><li>Networks over time are called “longitudi...
Networks in time <ul><li>Net>Transform>Generate in Time </li></ul><ul><ul><li>Use 2 - 4 </li></ul></ul><ul><li>Previous </...
Affiliation Network <ul><li>Use: scotland.paj </li></ul><ul><li>What does it mean? </li></ul>
Affiliations <ul><li>One mode network </li></ul><ul><li>Two mode network  </li></ul>
Experiment <ul><li>Create one mode of directors. </li></ul><ul><li>Create one mode of banks. </li></ul><ul><li>Check out [...
The Sawmill
Degree centrality <ul><li>The degree centrality of a vertex is its degree </li></ul><ul><li>Degree centralization of the n...
Distance <ul><li>A  geodesic  is the shortest path between two verticies </li></ul><ul><li>The  distance  from vertex u to...
Closeness <ul><li>The  closeness centrality  of a vertex is the number of other vertices divided by the sum of all distanc...
Closeness application <ul><li>Net>Transform>Edges>Arcs </li></ul><ul><li>Net>Partitions>Degree </li></ul><ul><li>Net>Trans...
Two more operations <ul><li>Net>Paths between 2 vertices>All Shortest </li></ul><ul><li>Net>Vector>Centrality>Closness </l...
Exercise <ul><li>What will happen to the network if Juan (HM-1) disappears?  Remove the vertex, compare closeness centrali...
Betweenness <ul><li>The betweenness centrality of a vertex is the proportion of all geodesics between pairs of other verti...
Betweenness Application <ul><li>Net>Vector>Centrality>Betweeness </li></ul>
Exercise <ul><li>Compute and draw the betweenness of the sawmill network. </li></ul>
Bridges <ul><li>A  bridge  is a line whose removal increases the number of components in the network. </li></ul><ul><li>De...
Bi-Components <ul><li>A  bi-component  is a component of minimum size 3 that does not contain a cut-vertex. </li></ul>
Strike Network
Bi-Components <ul><li>Net>Components>Bi-Components </li></ul><ul><ul><li>Use “2” to identify bridges </li></ul></ul><ul><u...
Ego-Networks, Constraint <ul><li>The ego-networks of a vertex contains the vertex, its neighbors, and all lines among the ...
Dyadic Constraint <ul><li>The dyadic constraint on a vertex  u  exercised by a tie between vertices  u  and  v  is the ext...
Structural Holes <ul><li>Net>Vector>Structural Holes </li></ul><ul><li>Options>Values of Lines>Similarities </li></ul><ul>...
Structural Holes 2 <ul><li>Net>Vector>Clustering Coefficients>CCI </li></ul><ul><ul><li>Look at Vector: Clustering Coeffic...
Constraint <ul><li>Operations>Transform>Remove Lines>Between Clusters </li></ul><ul><li>Net>Vector>Structural Holes </li><...
Diffusion <ul><li>Draw->Draw Partition (ModMath.net) </li></ul><ul><li>Layers> in y direction </li></ul><ul><li>Move>Fix>y...
Contagion <ul><li>The adoption rate is the number or percentage of new adoptors at a particular moment. </li></ul><ul><li>...
Exposure and Thresholds <ul><li>The  exposure  of a vertex in a network at a particular moment is the proportion of the ne...
Critical Mass <ul><li>The critical mass of a diffusion process is the minimum number of adopters needed to sustain a diffu...
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Social Network Based Information Systems (Tin180 Com)

  1. 1. Social Network Based Information Systems Don Steiny University of Oulu, Finland
  2. 2. Class goals <ul><li>Become familiar with techniques for analyzing social networks </li></ul><ul><li>Learn some of the problems that can be solved using SNA. </li></ul><ul><li>Learn some of the techniques used to solve problems in SNA. </li></ul><ul><li>Give a grounding for further learning. </li></ul>
  3. 3. Today <ul><li>Get acquainted </li></ul><ul><ul><li>I’ll really introduce myself </li></ul></ul><ul><ul><li>I will meet each of you. </li></ul></ul><ul><li>Overview of the papers you are getting. </li></ul><ul><li>Overview of the major subjects in social networks we are going to cover and why they are important. </li></ul><ul><li>Other resources. </li></ul><ul><li>Your networks </li></ul><ul><li>First Social Network Analysis using Pajek.. </li></ul>
  4. 4. Papers <ul><li>The Strength of Weak Ties - Mark Granovetter </li></ul><ul><li>An Experimental Study of the Small Worlds Problem - Jeffrey Travers; Stanley Milgram </li></ul><ul><li>Scale Free Networks - Albert-László Barabási and Eric Bonabeau </li></ul><ul><li>Social Networks and Loss of Capital - Wayne E. Baker, Robert R. Faulkner </li></ul>
  5. 5. More Papers <ul><li>The Diffusion of an Innovation among Physicians - James Colman, Elihu Katz, Herbert Menzel </li></ul><ul><li>Collaboration Networks, Structural Holes and Innovation: A Longitudinal Study - Gautam Ahuja </li></ul><ul><li>Social Process and Hierarchy Formation - Ivan Chase </li></ul><ul><li>The Impact of Social Structure on Economic Outcomes - Mark Granovetter </li></ul>
  6. 6. Still more papers <ul><li>The Iron Cage Revisited: Institutional Isomorphism and Collective Rationality in Organizational Fields - Paul J. DiMaggio, Walter W. Powell </li></ul><ul><li>Social Networks,the Tertius Iungens Orientation, and Involvement in Innovation - David Obstfeld </li></ul><ul><li>The Social Origin of Good Ideas - Ron Burt </li></ul><ul><li>The Sources and Consequences of Embeddedness for Economic Performance of Organizations: The Network Effect - Brian Uzzi </li></ul>
  7. 7. More papers yet <ul><li>From Community of Innovation to Community of Inertia - The Rise and Fall of the U.S. Tire Industry - Donald N. Sull </li></ul><ul><li>*Being No One - The Self-Model of Subjectivity - Thomas Metzinger </li></ul><ul><li>Embeddedness in the Making of Financial Capital: How Social Relations and Networks Benefit Firms Seeking Financing - Brian Uzzi </li></ul>
  8. 8. Whew, last of papers <ul><li>*What Creates Energy in Organizations - Rob Cross and Andrew Parker </li></ul><ul><li>World Society and the Nation State - John W. Meyer; John Boli; George M. Thomas, Francisco. O Ramirez </li></ul><ul><li>* - PAPERS WITH ASTRICK (*) are not eligible for course paper. </li></ul>
  9. 9. Who Does What? <ul><li>Anthropologists – kinship relations, friendship gift giving </li></ul><ul><li>Social psychologists – affections </li></ul><ul><li>Political Scientists – power relations </li></ul><ul><li>Economists – trade and organizational relations </li></ul><ul><li>Sociologists – Social choices </li></ul>
  10. 10. Some terms <ul><li>A graph is a set of vertices and a set of lines between pairs of vertices. </li></ul><ul><li>A vertex (singular of vertices) is the smallest unit in a network. </li></ul><ul><li>A line is a relation between two vertices in a network.. A line is defined by its two endpoints, which are the two vertices that are incident with the line. </li></ul><ul><li>A loop is a special kind of line, namely a line which connects a vertex to itself. </li></ul><ul><li>An arc is an ordered pair of vertices in which the first vertex is the sender (the tail of the arc) and the second the receiver of the relation (the head of the arc). </li></ul><ul><li>An edge , which has no direction, is represented by an unordered pair. It does not matter which vertex is first or second in the pair. </li></ul><ul><li>A directed graph or digraph contains one or more arcs. </li></ul><ul><li>An undirected graph does not contain arcs: all of its lines are edges. </li></ul><ul><li>A simple undirected graph contains neither multiple edges nor loops. </li></ul><ul><li>A simple directed graph does not contain multiple arcs. </li></ul><ul><li>A network consists of a graph and additional information on the vertices or the lines of the graph. </li></ul>
  11. 11. Our personal networks <ul><li>4 work sheets </li></ul><ul><li>Draw the network </li></ul><ul><li>Discussion </li></ul>
  12. 12. Dining Table Partners
  13. 13. Pajek data files <ul><li>.net – network files </li></ul><ul><li>.clu – partition files </li></ul><ul><li>.vec – vector files </li></ul><ul><li>.paj – project files </li></ul>
  14. 14. Pajek Data File <ul><li>*Vertices 26 </li></ul><ul><li>1 &quot;Ada&quot; 0.1646 0.1077 0.5000 </li></ul><ul><li>2 &quot;Cora&quot; 0.0481 0.3446 0.5000 </li></ul><ul><li>3 &quot;Louise&quot; 0.3472 0.0759 0.5000 </li></ul><ul><li>4 &quot;Jean&quot; 0.1063 0.6284 0.5000 </li></ul><ul><li>[…] </li></ul><ul><li>25 &quot;Laura&quot; 0.5101 0.6557 0.5000 </li></ul><ul><li>26 &quot;Irene&quot; 0.7478 0.9241 0.5000 </li></ul><ul><li>*Arcs </li></ul><ul><li>1 3 2 </li></ul><ul><li>1 2 1 </li></ul><ul><li>2 1 1 </li></ul><ul><li>2 4 2 </li></ul><ul><li>3 9 1 </li></ul><ul><li>3 11 2 </li></ul><ul><li>[…] </li></ul><ul><li>25 15 1 </li></ul><ul><li>25 17 2 </li></ul><ul><li>26 13 1 </li></ul><ul><li>26 24 2 </li></ul><ul><li>*Edges </li></ul>
  15. 15. Pajek files <ul><li>Let’s find the file Dining-table_partners.net, take a look at it with notepad. </li></ul>
  16. 16. Pajek Main Screen
  17. 17. Convert arcs to edges
  18. 18. Report Screen
  19. 19. Dialogue Box Info->Network->General
  20. 20. Draw Screen
  21. 21. Draw Screen Experience <ul><li>Load the file “dining_table_partners.net” and go through the handout labeled “Draw Screen” and do the commands there. </li></ul><ul><li>Dichotomize the network and draw it. </li></ul><ul><li>Remove all second choices and draw the network. </li></ul><ul><li>Use the factor option of Fruchterman Reingold to make a clearer distinction between the center and the periphery. </li></ul>
  22. 22. Networks as matrices – joke network
  23. 23. Matrix of joke network
  24. 24. Thinking about matrices <ul><li>How would the matrix be different if it was an undirected graph? </li></ul><ul><li>How would you represent values for the lines? </li></ul>
  25. 25. Create Pajek file from joke network <ul><li>Translates graphs into a simple file format </li></ul><ul><li>Usually this is automated </li></ul><ul><li>Use Pajek to create the network – hard work. </li></ul><ul><li>How could Excel, Access, SQL or other programs be used to generate networks? </li></ul>
  26. 26. Compare networks <ul><li>Generate random networks with the same number of nodes as the dining table partners network. </li></ul><ul><li>Use Draw->Info->All Properties to compare crossing lines. What is the systematic difference? </li></ul>
  27. 27. SNA Measurements <ul><li>Prevalent SNA measures at the </li></ul><ul><li> Individual level: centrality and prestige and roles such as isolates, liaisons, bridges, etc. </li></ul><ul><li> degree centrality – activity </li></ul><ul><li> closeness centrality – access to resources </li></ul><ul><li> betweenness centrality – control </li></ul><ul><li> eigenvector centrality – overall influence </li></ul><ul><li> D yadic level: distance and reachability, structural and other notions of equivalence, and </li></ul><ul><li>tendencies toward reciprocity. </li></ul><ul><li> T riadic level: balance and transitivity </li></ul><ul><li> S ubset level: cliques, cohesive subgroups, components </li></ul><ul><li> N etwork level: connectedness, diameter, centralization, density etc. </li></ul><ul><li>[Wasserman, S. and K. Faust, 1994, Social Network Analysis. ] </li></ul>
  28. 28. Partitions <ul><li>A partition of a networks is a classification or clustering of the vertices in the networks such that each vertex is assigned to exactly one class or cluster. </li></ul>
  29. 29. World System <ul><li>Go through the “World System” example </li></ul><ul><li>Open the trade network and energize the positions of the core countries only. Hint: create a new partition where core countries belong to class zero and others to class one or higher and energize it with Fix selected networks command. </li></ul>
  30. 30. World System
  31. 31. Trade Within South America – local view
  32. 32. Trade between continents – global view
  33. 33. World System Positions in South America – global view
  34. 34. Contextual view
  35. 35. World System GDP Vector
  36. 36. Fun with partitions <ul><li>There are several partition exercises we will work on now. </li></ul>
  37. 37. File: Attiro.net <ul><li>Load Attiro.net </li></ul>
  38. 38. Visiting Ties in Attiro
  39. 39. Density and Degree <ul><li>Density is the number of lines in a simple network expressed as a proportion of the maximum number of lines. </li></ul><ul><li>A complete network is a network of maximum density. </li></ul><ul><li>The degree of a vertex is the number of lines incident with it. </li></ul>
  40. 40. Degree measures <ul><li>Info>Network>General </li></ul><ul><li>Net>Transform>Arcs>Edges>All </li></ul><ul><li>File>Network>Save </li></ul><ul><li>Net>Partitions>Degree </li></ul><ul><li>Info>Partition </li></ul><ul><li>Partition>Make Vector </li></ul><ul><li>Info>Vector </li></ul>
  41. 41. Exercise – Compare Networks <ul><li>Compare the network SanJuanSur.net to the Attiro network. Is this network more cohesive? </li></ul>
  42. 42. Ajacent, indegree, outdegree <ul><li>Two vertices are adjacent if they are connected by a line. </li></ul><ul><li>The indegree of a vertex is the number of arcs it receives. </li></ul><ul><li>The outdegree is the number of arcs it sends. </li></ul>
  43. 43. Semiwalks and walks <ul><li>A semiwalk from vertex u to vertex v is a sequence of lines such that the end vertex of one line is the starting vertex of the next line and the sequence starts at vertex u and ends at vertex v. </li></ul><ul><li>A walk is a semiwalk with the additional condition that none of its lines are an arc of which the end vertex is the arc’s tail. </li></ul>
  44. 44. Paths and Semipaths <ul><li>A semipath is a semiwalk in which no vertex in between the first and last vertex of the semiwalk occurs more than once. </li></ul><ul><li>A path is a walk in which no vertex in between the first and last vertex of the walk occurs more than once. </li></ul>
  45. 45. Connection <ul><li>A network is (weakly) connected if each pair of vertices is connected by a semipath. </li></ul><ul><li>A networks is strongly connected if each pair of vertices is connected by a path. </li></ul>
  46. 46. Weak and Strong Components <ul><li>A (weak) component is a maximal (weakly) connected subnetworks. </li></ul><ul><li>A strong component is a maximal strongly connected subnetwork. </li></ul>
  47. 47. Find components: Attiro.net <ul><li>Net>Components>Strong (raise number to eliminate uninteresting components) </li></ul><ul><li>Draw>Draw-Partition </li></ul><ul><li>Net>Components>Weak </li></ul>
  48. 48. Cores <ul><li>A k-core is a maximal subnetwork in which every vertex has at least degree k within the subnetwork. </li></ul>
  49. 49. K-cores in Attiro visting network
  50. 50. Extracting k-cores <ul><li>Net>Partitions>Core>Input,Output,All </li></ul><ul><li>Operations>Extract from Network>Partition </li></ul><ul><li>Net>Components>Strong </li></ul>
  51. 51. Exercise: Extract k-cores <ul><li>Determine the k-cores in the network ExerciseII.net and extract the 4-core from the network. </li></ul>
  52. 52. Cliques <ul><li>A clique is a maximal complete subnetwork containing 3 vertices or more. </li></ul>
  53. 53. Clique detection (Attiro.net) <ul><li>Net>Transform>Arcs>Edges>All </li></ul><ul><li>Nets>First Network,Second Network </li></ul><ul><ul><li>2 nd : triad_undir.net </li></ul></ul><ul><li>Nets>Fragment (1 in 2)>Find </li></ul><ul><li>Nets>Fragment (1 in 2)>Options </li></ul><ul><ul><li>Extract Subnetwork checked </li></ul></ul><ul><li>File>Hierarchy>Edit </li></ul><ul><li>Info>Partitions </li></ul>
  54. 54. Signed Graph <ul><li>A signed graph is a graph in which eash line carries either a positive or a negative number. </li></ul>
  55. 55. Cycles, semicycles <ul><li>A cycle is a closed path. </li></ul><ul><li>A semicycle is a closed semipath. </li></ul><ul><li>A (semi)-cycles is balanced if it does not contain an uneven number of negative arcs. </li></ul>
  56. 56. Eight possible triadic constellations
  57. 57. Determining the balance of a relationship
  58. 58. Tendency towards balance
  59. 59. Clustering <ul><li>A cycle or semicycle is clusterable if it does not contain exactly one negative arc. </li></ul><ul><li>A signed graph is clusterable if it can be partitioned into clusters such that all positive ties are contained within clusters and all negative ties are situated between clusters. </li></ul>
  60. 60. Balance in the Monastery
  61. 61. Computing Balance <ul><li>[Draw]>Options>Values of Lines>Similarities </li></ul><ul><li>Partitions>Create Random Partition (3 clusters) </li></ul><ul><li>Operations>Balance (>100) – try several times. </li></ul>
  62. 62. Three solutions with one error
  63. 63. Balance over time <ul><li>Groups tend towards balance over time </li></ul><ul><li>Networks over time are called “longitudinal” </li></ul>
  64. 64. Networks in time <ul><li>Net>Transform>Generate in Time </li></ul><ul><ul><li>Use 2 - 4 </li></ul></ul><ul><li>Previous </li></ul><ul><li>Next </li></ul><ul><li>Options Previous/Next>Apply to </li></ul><ul><li>Options Previous/Next>Optimize Layouts </li></ul>
  65. 65. Affiliation Network <ul><li>Use: scotland.paj </li></ul><ul><li>What does it mean? </li></ul>
  66. 66. Affiliations <ul><li>One mode network </li></ul><ul><li>Two mode network </li></ul>
  67. 67. Experiment <ul><li>Create one mode of directors. </li></ul><ul><li>Create one mode of banks. </li></ul><ul><li>Check out [Draw]>Options>Lines>Different Widths </li></ul>
  68. 68. The Sawmill
  69. 69. Degree centrality <ul><li>The degree centrality of a vertex is its degree </li></ul><ul><li>Degree centralization of the network is the variation in the degrees of verticies divided by the maximum degree variation which is possible in a network of the same size. </li></ul>
  70. 70. Distance <ul><li>A geodesic is the shortest path between two verticies </li></ul><ul><li>The distance from vertex u to vertex v is the length of the geodesic from u to v. </li></ul>
  71. 71. Closeness <ul><li>The closeness centrality of a vertex is the number of other vertices divided by the sum of all distances between the vertex and all others. </li></ul><ul><li>Closeness centralization is the variation in the closeness centrality of vertices divided by the maximum variation in closeness centrality scores possible in a network of the same size. </li></ul>
  72. 72. Closeness application <ul><li>Net>Transform>Edges>Arcs </li></ul><ul><li>Net>Partitions>Degree </li></ul><ul><li>Net>Transform>Remove>multiple lines </li></ul><ul><li>Net>Transform>Remove>loops </li></ul><ul><li>Net>k-neighbours </li></ul><ul><li>Net>Paths between 2 vertices>All shortest </li></ul><ul><li>Net>Vector>Centrality>Closeness </li></ul>
  73. 73. Two more operations <ul><li>Net>Paths between 2 vertices>All Shortest </li></ul><ul><li>Net>Vector>Centrality>Closness </li></ul>
  74. 74. Exercise <ul><li>What will happen to the network if Juan (HM-1) disappears? Remove the vertex, compare closeness centrality and centralization and interpret the results. </li></ul>
  75. 75. Betweenness <ul><li>The betweenness centrality of a vertex is the proportion of all geodesics between pairs of other vertices that include this vertex. </li></ul><ul><li>Betweenness centralization is the vairation in the betweenness centrality of vertices divided by the maximum vairiation in betweenness centrality scores possible in an network of the same size. </li></ul>
  76. 76. Betweenness Application <ul><li>Net>Vector>Centrality>Betweeness </li></ul>
  77. 77. Exercise <ul><li>Compute and draw the betweenness of the sawmill network. </li></ul>
  78. 78. Bridges <ul><li>A bridge is a line whose removal increases the number of components in the network. </li></ul><ul><li>Deleting a vertex from the network means that the vertex and all lines incident with the vertex are removed from the network. </li></ul><ul><li>A cut-vertex is a vertex whose deletion increase the number of components in the network. </li></ul>
  79. 79. Bi-Components <ul><li>A bi-component is a component of minimum size 3 that does not contain a cut-vertex. </li></ul>
  80. 80. Strike Network
  81. 81. Bi-Components <ul><li>Net>Components>Bi-Components </li></ul><ul><ul><li>Use “2” to identify bridges </li></ul></ul><ul><ul><li>“Vertices belonging to …” Isolates: 0, more than one (bridges): 9999998 </li></ul></ul><ul><ul><li>Articulation points: number of bridges to which a node belongs (0 – 0, 1 – 1, …) </li></ul></ul>
  82. 82. Ego-Networks, Constraint <ul><li>The ego-networks of a vertex contains the vertex, its neighbors, and all lines among the selected vertex. </li></ul>
  83. 83. Dyadic Constraint <ul><li>The dyadic constraint on a vertex u exercised by a tie between vertices u and v is the extent to which u has more and stronger ties with neighbors who are strongly connected to vertex v . </li></ul>
  84. 84. Structural Holes <ul><li>Net>Vector>Structural Holes </li></ul><ul><li>Options>Values of Lines>Similarities </li></ul><ul><li>Info>Vector </li></ul><ul><li>Vectors>Transform>Multiply By </li></ul><ul><li>[Draw]Options>Size of Vertices </li></ul><ul><li>Net>k-neighbors>All (from 1, distance 1) </li></ul><ul><li>Operations>Extract from Network>Partition (1) </li></ul><ul><li>[Main]Info>Network>General </li></ul>
  85. 85. Structural Holes 2 <ul><li>Net>Vector>Clustering Coefficients>CCI </li></ul><ul><ul><li>Look at Vector: Clustering Coefficients CC1 </li></ul></ul>
  86. 86. Constraint <ul><li>Operations>Transform>Remove Lines>Between Clusters </li></ul><ul><li>Net>Vector>Structural Holes </li></ul><ul><li>Operations>Brokerage Roles </li></ul><ul><li>Info>Partition </li></ul>
  87. 87. Diffusion <ul><li>Draw->Draw Partition (ModMath.net) </li></ul><ul><li>Layers> in y direction </li></ul><ul><li>Move>Fix>y </li></ul><ul><li>[Draw screen]Options>Transform>Rotate 2D </li></ul>
  88. 88. Contagion <ul><li>The adoption rate is the number or percentage of new adoptors at a particular moment. </li></ul><ul><li>Info>Partition </li></ul>
  89. 89. Exposure and Thresholds <ul><li>The exposure of a vertex in a network at a particular moment is the proportion of the neighbors who have adopted at that time. </li></ul><ul><li>The threshold of an actor is his or her exposure at the time of adoption. </li></ul>
  90. 90. Critical Mass <ul><li>The critical mass of a diffusion process is the minimum number of adopters needed to sustain a diffusion process. </li></ul><ul><li>A threshold lag is a period in which an actor does not adopt although he or she is exposed at the level at which he or she will adopt later. </li></ul>
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