How the Numbers Add UpWhen Connecting the Organisation   ‘Simply because your data links people and you can visualize that...
Some Numbers and Laws ‘Each of us is part of a large cluster, the worldwide social net, from which no one is left out. We ...
Dunbar’s numbers.    Dunbar, R 2010, How many friends does one person need? Dunbars number and other evolutionary quirks.,...
Unique Participants in a Network                                      (Dunbar’s and Wellman’s Numbers)                    ...
90-9-1 Community Participation Heuristic                      http://lithosphere.lithium.com/t5/Building-Community-the-Pla...
Network Laws in Social Situations              Cross, R, Parker, A & Sasson, L (eds) 2003, Networks in the knowledge econo...
So What?‘Whatever a central management imposes, informal networks develop in ways that shapehow an organisation works. The...
Communication in Practice                            Pentland A, ‘The New Science of Building Great Teams’, Harvard Busine...
Hierarchical Thinking                             Everyone understands the hierarchical view                              ...
Network Thinking    This network view is exactly the same as the hierarchical view                                      Th...
The Thinking Shift Allows Us To Do This                                      This view does allow for cross-branch communi...
So how do we get …                                                       1                                            From...
A Quick Centrality Lesson  ‘In all businesses there are two organisations: one that is shown on the formal  organisation c...
Sizing by degree centrality                                                           (an activity measure)               ...
Sizing by closeness centrality                                                         (a proximity measure)              ...
Sizing by betweenness centrality                                                         (a position measure)             ...
Sizing by eigenvector centrality                                                     (an advantage measure)               ...
Boundary Specification and Sample Size                                               Required for 95% Confidence          ...
Moving to a SolutionAttributing the Network ‘Simplicity is the key to effective scientific inquiry.’                      ...
Many networks look like this                          Which of the aforementioned measures can you use on this network?Cop...
Attributing Data Using Behaviour (B is the person).                          Wassermann, S & Faust, K 1999, Social network...
Attributing Data Using RolesCoordinator - a person who brokers connections within the    A   B   Csame group or team.Gatek...
Allows us to do this ...                  Information Network > weeklyIs the engagement dynamic appropriate and effective?...
And this …                 Program Evaluation (Comparative Organisational Dynamic)1. Data has been normalised to allow com...
And this ….                                  Program Evaluation (Comparative Brokerage)1. Data has been normalised to allo...
Applying a metric                                                      messages sent – messages received                 C...
Changes the network analysis from this …Copyright © 2012 – HyperEdge Pty Ltd              27
To this …                     No Discernible Role                                                                         ...
Or even this …Copyright © 2012 – HyperEdge Pty Ltd                    29
And in turn allows deeper analysis like this …           Escort and Expediter Network Sized for Betweenness (Bridges)     ...
And greater understanding like this …                        Escort and Expediter Network Consultant Brokerage            ...
Summary‘A good deal of the corporate planning I have observed is like a ritual rain dance; it has noeffect on the weather ...
Summary.      Social network analysis, done properly, provides:          – a powerful quantitative, qualitative, and visu...
Books       http://www.amazon.com/dp/B008YPL6W4           Available January 2013Copyright © 2012 – HyperEdge Pty Ltd      ...
For more details please visit our website at www.hyperedge.com.au.Example reports can be found at:      http://www.hypered...
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Durnat law numbers

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Durnat law numbers

  1. 1. How the Numbers Add UpWhen Connecting the Organisation ‘Simply because your data links people and you can visualize that, it does not mean you have performed network analysis. This is akin to displaying a line plot of some stocks price over a quarter and claiming you have performed statistical analysis – all you have done is report data! As with all other statistical processes, network analysis is meant to draw meaning and inference from the structure, which requires an understanding of these methodologies, their strengths and limitations’. Drew Conway, Political Scientist, 2009. Copyright © 2012: HyperEdge Pty Ltd
  2. 2. Some Numbers and Laws ‘Each of us is part of a large cluster, the worldwide social net, from which no one is left out. We do not know everyone on this globe, but it is guaranteed that there is a path between any two of us in this web of people’. Professor Albert-Laszlo Barabasi, Physicist, 2002 Copyright © 2012: HyperEdge Pty Ltd 2
  3. 3. Dunbar’s numbers. Dunbar, R 2010, How many friends does one person need? Dunbars number and other evolutionary quirks., Faber and Faber, London. 650 1,448 270 708 127 338 Increasing Acquaintances 85 152 Connections Extended 35 68 Close 18 33 Immediate 10 15 Increasing Intimacy Intimate 5 5Dunbar’s Numbers are an indicator of meaningful relationships and the maximum effective number of people in a network. Theusually accepted number is 152. There is an mega-band number of around 700, and an upper limit of about 1,500.Copyright © 2012: HyperEdge Pty Ltd 3
  4. 4. Unique Participants in a Network (Dunbar’s and Wellman’s Numbers) Wellman’s Number Dunbar’s Number Dunbar, R 2010, How many friends does one person need? Dunbars number and other evolutionary quirks., Faber and Faber, London. Wellman, B 2011, Is Dunbars Number up?, British Journal of Psychology, pp. 1-3.Copyright © 2012: HyperEdge Pty Ltd 4
  5. 5. 90-9-1 Community Participation Heuristic http://lithosphere.lithium.com/t5/Building-Community-the-Platform/The-90-9-1-Rule-in-Reality/ba-p/5463 A 2010 study by Dr Michael Wu, using ten years of data from more than 200 online communities, found that: – 90% of all users are “lurkers” who don’t actively contribute. – 9% of all users are “occasional contributors” providing less than 50% of the content. – 1% of all users are “hyper- contributors” providing greater than 50% of the content. Using this heuristic the predicted size of the discussion group was 2,420 people. (The actual number was 2,643).Copyright © 2012: HyperEdge Pty Ltd 5
  6. 6. Network Laws in Social Situations Cross, R, Parker, A & Sasson, L (eds) 2003, Networks in the knowledge economy, Oxford University Press, New York.• Law of Emergence - Relationships are unimpeded by pre-ordained formal structures.• Law of Propinquity - Those close by form a tie. The probability of two people communicating is inversely proportional by a factor of 2 to the distance between them.• Law of Oligarchy - Birds of a feather flock together. Social strata fulfilling particular functions tend to become isolated over time.• Law of Links - The number of possible links in a social system = N(N-1) or sometimes N(N-1)/2. 152 nodes = 22,952 links!Copyright © 2012: HyperEdge Pty Ltd 6
  7. 7. So What?‘Whatever a central management imposes, informal networks develop in ways that shapehow an organisation works. These multiple networks involve information-flow,knowledge transfer, work cooperation, support, friendship and antagonisms. They arecrucial to organisational functioning’. Professor Garry Robins, Network Scientist, Melbourne University, 2006 Copyright © 2012: HyperEdge Pty Ltd 7
  8. 8. Communication in Practice Pentland A, ‘The New Science of Building Great Teams’, Harvard Business Review, April 2012 A 2011 study of 2,500 participants by the Massachusetts Institute of Technology found that the most important predictor of team success is in its communication patterns. Of note the study found that: – communication patterns are as significant as all other factors, including intelligence, personality, and talent combined; – researchers could foretell which teams would out- perform the others simply by looking at the data on their communication patterns, even without meeting the team members; – connectivity, activity, and energy were the key 1 A communication dynamics that enabled or effected performance; r ij A ji – mapping communication behaviours over time, and m ij making small adjustments to move it closer to the ideal, dramatically improves team performance.Copyright © 2012: HyperEdge Pty Ltd 8
  9. 9. Hierarchical Thinking Everyone understands the hierarchical view This view does not allow for cross-branch communicationCopyright © 2012: HyperEdge Pty Ltd 9
  10. 10. Network Thinking This network view is exactly the same as the hierarchical view This view could allow for cross-branch communicationCopyright © 2012: HyperEdge Pty Ltd 10
  11. 11. The Thinking Shift Allows Us To Do This This view does allow for cross-branch communication. Note what is different.Copyright © 2012: HyperEdge Pty Ltd 11
  12. 12. So how do we get … 1 From: r   AijAji m ij To: And add further understanding without complicating the output?Copyright © 2012: HyperEdge Pty Ltd 12
  13. 13. A Quick Centrality Lesson ‘In all businesses there are two organisations: one that is shown on the formal organisation chart and another that exists in reality. The latter is made up of not job titles or formal lines of authority, but rather influencers and other individuals.’ Doctor Neil Farmer, Network Scholar and Author, 2008 Copyright © 2012: HyperEdge Pty Ltd 13
  14. 14. Sizing by degree centrality (an activity measure) Commentators (receivers and transmitters) - degree centrality n Where ki is the degree of node i; ki   Aij n is the number of nodes; Aij is an adjacency matrix; and ij denotes a tie between nodes i j 1 and j. n k iin   Aij In-degree is the number of ties directed towards the node. j 1 Reveals how much activity is People at the centre of the going on and who are the network: most active members by • are the connector or hub of n   Aij counting the number of direct the network, out links each person has to others in the network. • may be in an advantaged position in the network. k j Out-degree is the number of outgoing ties from the node. Does not necessarily describe • are usually less dependent on other individuals. i 1 power or influence. • are often a deal maker or broker.Copyright © 2012 – HyperEdge Pty Ltd 14
  15. 15. Sizing by closeness centrality (a proximity measure) Where li is the mean distance; 1 li   dij Conduits n is the total number of nodes; (providers and seekers) - closeness centrality and dij is the length of the n j shortest path between nodes i and j in a matrix. • Closeness centrality begins with the assumption that having short paths to other nodes increases the influence in the network of that node. • It measures the average distance a node is from all other nodes in a network, and therefore is a proximity measure. • Unconnected nodes by definition have an Highlights people with the shortest paths to other people, thus allowing them to directly pass on and receive communications infinite distance between them, which means quicker than others in the organisation. scores cannot be computed for isolated Is strongly correlated with organisational influence if the nodes. individual is a skilled communicator. • Closeness centrality requires the network, or These individuals are often network brokers. They are often the ‘pulse-takers’ of the organisation. at least the component under examination, to be complete.Copyright © 2012 – HyperEdge Pty Ltd 15
  16. 16. Sizing by betweenness centrality (a position measure) Where xi is the betweenness of i Controllers n xi   node i; is the number of paths (brokers and gatekeepers) - betweenness centrality st from node s to node t that pass through node i; and gst is the st gst number of paths from node s to node t. • Betweenness centrality measures the extent that a node lays on the path of other nodes. • Betweenness centrality is unlike other centrality measures because it does not measure how well the node in question is connected, but rather how it connects components of the network. • It is a proxy for understanding strategicReveals individuals who: Identifies the bridges within position within the network.• connect disparate groups the network. They may act as within the network. the true gatekeeper deciding • It can be applied to both directed and• hold a favoured or what does or does not get powerful position in the passed through the network, undirected networks. network. or as the “third who benefits”• have great influence over by passing information to what is communicated others to secure advantage. through the network. .• act as intermediariesCopyright © 2012 – HyperEdge Pty Ltd 16
  17. 17. Sizing by eigenvector centrality (an advantage measure) Where xi is the centrality of each Connectors xi  k 1 A x node i; k is the eigenvalue, with 1 eigenvector centrality 1 ij j being the largest and -1 the smallest; Aij is an adjacency j matrix; and ij denotes a tie between nodes i and j. • Eigenvector centrality begins with the assumption that having connections with other central nodes increases the relative importance of that node. • A high eigenvector centrality score means the node is important because either it is connected to many nodes, or is connected to a few very highly connected nodes Measures how well connected a person is and how much direct • Eigenvector centrality has the limitation that it influence they may have over the most active people in the works best on undirected networks. network Measures how close a person is to other highly connected people in terms of the global or overall makeup of the network Is a reasonable measure of “network positional advantage” and/or perceived power.Copyright © 2012 – HyperEdge Pty Ltd 17
  18. 18. Boundary Specification and Sample Size Required for 95% Confidence Total Number Required Required of People Precision Precision + or – 5% + or – 10% 50 44 33 75 63 42 100 80 49 150 108 59 200 132 65 300 168 73 400 196 78 500 217 81 Russ-Eft, D & Preskill, H 2010, Evaluation in organizations: A systematic approach to enhancing learning, performance and change, Pereus Books Group, New York.Copyright © 2012 – HyperEdge Pty Ltd 18
  19. 19. Moving to a SolutionAttributing the Network ‘Simplicity is the key to effective scientific inquiry.’ Professor Stanley Milgram, Sociologist, 1973 Copyright © 2012: HyperEdge Pty Ltd 19
  20. 20. Many networks look like this Which of the aforementioned measures can you use on this network?Copyright © 2012 – HyperEdge Pty Ltd 20
  21. 21. Attributing Data Using Behaviour (B is the person). Wassermann, S & Faust, K 1999, Social network analysis, Cambridge University Press, Cambridge. Isolate - a person that has no links. A B C A B C Receiver - a person that has only in-links. Transmitter - a person that has only out-links A B C and no in-links. Carrier - a person that has an equal number of A B C in-links and out-links. Other - a person that does not fall into the A B C previous categories.Copyright © 2012 – HyperEdge Pty Ltd 21
  22. 22. Attributing Data Using RolesCoordinator - a person who brokers connections within the A B Csame group or team.Gatekeeper - a person who transmits information and other A B Cresources to the same group or team from sourcesexternal to that group or team.Representative - a person who transmits information and A B Cother resources from their group or team to an externalgroup or team.Consultant - a person who intermittently takes the central A B Clead by connecting others in the same group or team, butwho belongs to another group or team.Liaison - a person who transmits information and other A B Cresources from one group or team to another group orteam, whilst themselves belonging to a different group orteam. Copyright © 2012 – HyperEdge Pty Ltd 22
  23. 23. Allows us to do this ... Information Network > weeklyIs the engagement dynamic appropriate and effective? Copyright © 2012 – HyperEdge Pty Ltd 23
  24. 24. And this … Program Evaluation (Comparative Organisational Dynamic)1. Data has been normalised to allow comparisons.2. The bottom and top of the boxes are the 25th and 75th percentiles (the lower and upper quartiles, respectively), and the black band in the box is the 50th percentile (the median).3. Diamonds indicate the mean, and red circles and crosses are outliers. Copyright © 2012 – HyperEdge Pty Ltd 24
  25. 25. And this …. Program Evaluation (Comparative Brokerage)1. Data has been normalised to allow comparisons.2. The bottom and top of the boxes are the 25th and 75th percentiles (the lower and upper quartiles, respectively), and the black band in the box is the 50th percentile (the median).3. Diamonds indicate the mean, and red circles and crosses are outliers. Copyright © 2012 – HyperEdge Pty Ltd 25
  26. 26. Applying a metric messages sent – messages received Contribution Index = messages sent + messages received If an individual only sends messages and receives none then their contribution index is +1.000 If an individual only receives messages and sends none then their contribution index is -1.000 If the communication behaviour is balanced then the contribution index is 0.000 Sender +1 Envoi Expediter Contribution Escort Contribution Index Frequency Expert Receiver -1Gloor, P 2006, Swarm creativity: Competitive advantage through collaborative innovation networks, Oxford University Press, Oxford. Copyright © 2012 – HyperEdge Pty Ltd 26
  27. 27. Changes the network analysis from this …Copyright © 2012 – HyperEdge Pty Ltd 27
  28. 28. To this … No Discernible Role Envoi Escort Expert Expediter1. The links inside the “circles” are posts between like roles. Note there are no posts between Experts.2. The thicker curves linking groups are consolidated exchanges between groups. They do not show frequency, or links from one individual to another.3. Note the relative density in the Escort and Expediter groups. Copyright © 2012 – HyperEdge Pty Ltd 28
  29. 29. Or even this …Copyright © 2012 – HyperEdge Pty Ltd 29
  30. 30. And in turn allows deeper analysis like this … Escort and Expediter Network Sized for Betweenness (Bridges) Larger nodes have greater betweenness within their group, and therefore a better strategic position within the network.Copyright © 2012 – HyperEdge Pty Ltd 30
  31. 31. And greater understanding like this … Escort and Expediter Network Consultant Brokerage A B C Larger nodes have greater betweenness within their group, and therefore a better strategic position within the network, but note who holds the consultant roles.Copyright © 2012 – HyperEdge Pty Ltd 31
  32. 32. Summary‘A good deal of the corporate planning I have observed is like a ritual rain dance; it has noeffect on the weather that follows, but those who engage in it think it does. Moreover, itseems to me that much of the advice and instruction related to corporate planning isdirected at improving the dancing, not the weather’ Emeritus Professor James Brian Quinn, Tuck School of Business, Dartmouth College, 1980. Copyright © 2012 – HyperEdge Pty Ltd 32
  33. 33. Summary. Social network analysis, done properly, provides: – a powerful quantitative, qualitative, and visual diagnostic, – empirical information on the “real or shadow” structures and relationships in an organisation, – a means to reach shared understanding and common meaning, – a baseline for organisational and personal improvement. The key is “done properly”! You cannot escape the mathematics! Use the right tool and presentation for the job, and remember visualisation is not analysis. Whatever your approach ensure you have multiple lines of evidence. For example, narrative provide additional granularity and allow for data triangulation and validation. Above all else you must understand your organisation, the data, the resultant network and visualisations, and the assumptions you are making.Copyright © 2012 – HyperEdge Pty Ltd 33
  34. 34. Books http://www.amazon.com/dp/B008YPL6W4 Available January 2013Copyright © 2012 – HyperEdge Pty Ltd 34
  35. 35. For more details please visit our website at www.hyperedge.com.au.Example reports can be found at: http://www.hyperedge.com.au/sites/default/files/Example_Org_Comm_Profile.pdf and, http://www.hyperedge.com.au/sites/default/files/Example_Pers_Comm_Profile.pdf.An eBook - Network Project Management - is available at: http://www.amazon.com/dp/B008YPL6W4.Graham Durant-Law+61 (0) 408 975 795graham@hyperedge.com.auHyperEdge Pty LtdPost Office Box 3076Manuka ACT 2603Australia Copyright © 2012 – HyperEdge Pty Ltd

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