How Numbers Connect Organisations

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.

Copyright © 2012: HyperEdge Pty Ltd

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

Dunbar’s numbers.
Dunbar, R 2010, How many friends does one person need? Dunbar's 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 5

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.


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? 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.


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).


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!


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
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.


Hierarchical Thinking
Everyone understands the hierarchical view

This view does not allow for cross-branch communication


Network Thinking
This network view is exactly the same as the hierarchical view

This view could allow for cross-branch communication


The Thinking Shift Allows Us To Do This

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


So how do we get …

1
From: r   AijAji
m ij

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)

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

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.


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 strategic
Reveals 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 intermediaries


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.


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.


Moving to a Solution
Attributing the Network
‘Simplicity is the key to effective scientific inquiry.’
Professor Stanley Milgram, Sociologist, 1973


Many networks look like this

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.

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.


Attributing Data Using Roles
Coordinator - a person who brokers connections within the A B C
same group or team.

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

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

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

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

Allows us to do this ...

Information Network > weekly

Is the engagement dynamic appropriate and effective?


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.


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.


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 -1

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


Changes the network analysis from this …


To this …

No Discernible Role
Envoi
Escort

Expert

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 …

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 …

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.


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

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) 408 975 795
graham@hyperedge.com.au

HyperEdge Pty Ltd
Post Office Box 3076
Manuka ACT 2603
Australia

Copyright © 2012 – HyperEdge Pty Ltd

How Numbers Connect Organisations

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