durnat law numbers

How the Numbers Add Up When 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 stock's 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.

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Some Numbers and Laws

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‘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

Dunbar’s numbers.Dunbar, R 2010, How many friends does one person need? Dunbar's number and other evolutionary quirks., Faber and Faber, London.

3

Dunbar’s Numbers are an indicator of meaningful relationships and the maximum effective number of people in a network. The usually accepted number is 152. There is an mega-band number of around 700, and an upper limit of about 1,500.

650

270

127

85

35

18

10

5Intimate

Immediate

Close

Extended

Acquaintances

IncreasingIntimacy

IncreasingConnections

15

33

68

152

338

708

1,448

5


Unique Participants in a Network(Dunbar’s and Wellman’s Numbers)


Dunbar, R 2010, How many friends does one person need? Dunbar's number and other evolutionary quirks., Faber and Faber, London.

Wellman, B 2011, 'Is Dunbar's Number up?', British Journal of Psychology, pp. 1-3.

Dunbar’s Number

Wellman’s Number

90-9-1 Community Participation Heuristichttp://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).

Network Laws in Social SituationsCross, R, Parker, A & Sasson, L (eds) 2003, Networks in the knowledge economy, Oxford University Press, New York.

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• 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!


So What?


‘Whatever a central management imposes, informal networks develop in ways that shape how an organisation works. These multiple networks involve information-flow, knowledge transfer, work cooperation, support, friendship and antagonisms. They are crucial to organisational functioning’.

Professor Garry Robins, Network Scientist, Melbourne University, 2006

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 communication dynamics that enabled or effected performance;

– mapping communication behaviours over time, and making small adjustments to move it closer to the ideal, dramatically improves team performance.

8

1ij ji

ij

r A Am


Hierarchical ThinkingEveryone understands the hierarchical view

9

This view does not allow for cross-branch communication


Network ThinkingThis network view is exactly the same as the hierarchical view

10

This view could allow for cross-branch communication


The Thinking Shift Allows Us To Do This

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This view does allow for cross-branch communication.Note what is different.


So how do we get …

12

1ij ji

ij

r A Am

From:

To:

And add further understanding without complicating the output?


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

Sizing by degree centrality(an activity measure)

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Reveals how much activity is going on and who are the most active members by counting the number of direct links each person has to others in the network.

Does not necessarily describe power or influence.

People at the centre of the network:• are the connector or hub of

the network,• may be in an advantaged

position in the network.• are usually less dependent

on other individuals.• are often a deal maker or

broker.

Commentators(receivers and transmitters) - degree centrality

1

n

i ijj

k A

Where ki is the degree of node i; n is the number of nodes; Aij is an adjacency matrix; and ijdenotes a tie between nodes iand j.

1

nini ij

j

k A

In-degree is the number of ties directed towards the node.

1

noutj ij

i

k A

Out-degree is the number of outgoing ties from the node.

Sizing by closeness centrality(a proximity measure)


Highlights people with the shortest paths to other people, thus allowing them to directly pass on and receive communications quicker than others in the organisation.

Is strongly correlated with organisational influence if the individual is a skilled communicator.

These individuals are often network brokers. They are often the ‘pulse-takers’ of the organisation.

Conduits(providers and seekers) - closeness centrality

1i ij

j

l dn

Where li is the mean distance; n is the total number of nodes; and dij is the length of the shortest path between nodes iand 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 infinite distance between them, which means scores cannot be computed for isolated nodes.

• Closeness centrality requires the network, or at least the component under examination, to be complete.

Sizing by betweenness centrality(a position measure)


Reveals individuals who:• connect disparate groups

within the network.• hold a favoured or

powerful position in the network.

• have great influence over what is communicated through the network.

• act as intermediaries

Identifies the bridges within the network. They may act as the true gatekeeper deciding what does or does not get passed through the network, or as the “third who benefits” by passing information to others to secure advantage..

Controllers(brokers and gatekeepers) - betweenness centrality

ististst

nxg

Where xi is the betweenness of node i; is the number of paths from node s to node t that pass through node i; and gst is the 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 strategic position within the network.

• It can be applied to both directed and undirected networks.

Sizing by eigenvector centrality(an advantage measure)


Measures how well connected a person is and how much direct influence they may have over the most active people in the 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.

Connectorseigenvector centrality

11i ij j

j

x k A x Where xi is the centrality of each node i; k is the eigenvalue, with 1 being the largest and -1 the smallest; Aij is an adjacency 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

• Eigenvector centrality has the limitation that it works best on undirected networks.

Boundary Specification and Sample Size

Total Number of People

Required Precision+ or – 5%

Required Precision + 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

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Required for 95% Confidence

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

Moving to a SolutionAttributing the Network


‘Simplicity is the key to effective scientific inquiry.’Professor Stanley Milgram, Sociologist, 1973

Many networks look like this

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Which of the aforementioned measures can you use on this network?


Attributing Data Using Behaviour (B is the person).Wassermann, S & Faust, K 1999, Social network analysis, Cambridge University Press, Cambridge.

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Isolate - a person that has no links. A B C

A B C

A B C

A B CReceiver - a person that has only in-links.

Transmitter - a person that has only out-links and no in-links.

Carrier - a person that has an equal number of in-links and out-links.

Other - a person that does not fall into the previous categories.

A B C


Attributing Data Using Roles

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A B C

A CB

A CB

A B C

Gatekeeper - a person who transmits information and other resources to the same group or team from sources external to that group or team.

Representative - a person who transmits information and other resources from their group or team to an external group or team.

Liaison - a person who transmits information and other resources from one group or team to another group or team, whilst themselves belonging to a different group or team.

Coordinator - a person who brokers connections within the same group or team.

A CBConsultant - a person who intermittently takes the central lead by connecting others in the same group or team, but who belongs to another group or team.


Allows us to do this ...

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Information Network > weekly

Is the engagement dynamic appropriate and effective?


And this …Program Evaluation (Comparative Organisational Dynamic)

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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.


And this ….Program Evaluation (Comparative Brokerage)

25

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.


Applying a metric

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If an individual only sends messages and receives none then their contribution index is +1.000If an individual only receives messages and sends none then their contribution index is -1.000If the communication behaviour is balanced then the contribution index is 0.000

ContributionFrequency

ContributionIndex

Sender +1

Receiver -1

Expert

Envoi

Escort

Expediter

Gloor, P 2006, Swarm creativity: Competitive advantage through collaborative innovation networks, Oxford University Press, Oxford.

messages sent – messages received

messages sent + messages receivedContribution Index =


To this …

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No Discernible Role

Expert

EscortEnvoi

Expediter

1. 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.


Or even this …


And in turn allows deeper analysis like this …

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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.


And greater understanding like this …

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Escort and Expediter Network Consultant Brokerage

A CB

Larger nodes have greater betweenness within their group, and therefore a better strategic position

within the network, but note who holds the consultant roles.


Summary


‘A good deal of the corporate planning I have observed is like a ritual rain dance; it has no effect on the weather that follows, but those who engage in it think it does. Moreover, it seems to me that much of the advice and instruction related to corporate planning is directed at improving the dancing, not the weather’

Emeritus Professor James Brian Quinn, Tuck School of Business, Dartmouth College, 1980.

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.


Books

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http://www.amazon.com/dp/B008YPL6W4 Available January 2013


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 [email protected]

HyperEdge Pty LtdPost Office Box 3076Manuka ACT 2603Australia


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