CSE5656 Complex Networks - Dunbar's Number

Complex Networks Class
!
Dunbar’s Number
!
Marcello Tomasini
Bio-Complex Lab
Department of Computer Sciences
Florida Tech

Outline
•Introduction
•The Social Brain Hypothesis
•Validation
•Impact of Social Medias
•Social Implications
•Conclusion

Introduction
Robin I. M. Dunbar, professor of evolutionary
anthropology at the University of Oxford
!
“Human beings can hold only about 150
meaningful relationships in their heads.
Informally, it is the number of people you
wouldn’t feel embarrassed about joining if you
happened to find them at the bar of an airport
transit lounge at 3am” — Dunbar [1]
!
“There was a discussion by people saying ‘I’ve
got too many friends — I don’t know who half
these people are’. Somebody apparently said,
‘Look, there’s this guy in England who says you
can’t have more than 150’” — Dunbar [2]
[1] The magic number:
http://www.thersa.org/fellowship/journal/archive/spring-2010/features/the-magic-number
[2] Don't Believe Facebook; You Only Have 150 Friends:
http://www.npr.org/2011/06/04/136723316/dont-believe-facebook-you-only-have-150-friends !
Figure: http://www.technologyreview.com/news/428478/three-questions-for-robin-dunbar/

The Social Brain Hypothesis [3, 4]
Hypothesis: primates’ large brains reflect the computational
demands of the complex social systems that characterize the order
!
Large relative [to body] brain size correlates with greater cognitive
ability.
!
Because the cost of maintaining a large brain is great, it will evolve
only when the payoffs overcome the steep cost.
Possible explanations:
1.ecological function
2.uniquely complex nature of primate social life (social
function of intellect)
3.developmental (constrained by maternal metabolic rates)
!
Developmental hypothesis can be discarded because:
•offers no explanation of any kind as to why the brain should
grow to this limit
•validity has been questioned
[3] Dunbar, Robin IM. "Neocortex size as a constraint on group size in primates."
Journal of Human Evolution 22.6 (1992): 469-493.
[4] Dunbar, Robin IM. "The social brain hypothesis." brain 9.10 (1998): 178-190.

The Social Brain Hypothesis
Ecological hypothesis variables:
•frugivores need to monitor the availability of dispersed,
ephemeral food supply (% fruits)
•sheer size of the mental map in order to navigate from one
food source or refuge to another (ranging area)
•extractive foraging: removal of food items from an embedded
matrix (relative brain size)
!
Social hypothesis variables:
•number of individuals that an animal has to know and maintain
relationships with (group size is linear function of brain size)
•number of relationships with every other member of the group
and all the third party relationships between every possible
pair (group size is logarithmic function of brain size)
•nature if the relationships between individuals (cliques size is
logarithmic function of brain size)

Group size is found to be a function of relative neocortical
volume, but the ecological variables are not:

Remarks:
!
•number of neocortical neurons limits the organism’s
information processing capacity and that this then limits
the number of relationships an individual can monitor
simultaneously
!
•using the human neocortex volume to extrapolate a value
for group size from the primate equation produce a value
close to 150

Validation: Christmas Cards [5]
Examine social network size based on the exchange of Christmas
cards
!
Writing cards costs money and time thus implies that the
recipient are worth the effort
!
Consider passive factors (distance, work colleague, overseas) and
active factors (emotional closeness, genetic relatedness)
[5] Hill, Russell A., and Robin IM Dunbar. "Social network size in humans." Human
nature 14.1 (2003): 53-72.

Validation: Christmas Cards
Remarks:
•mean network size is within the confidence interval for human
group sizes predicted on the basis of the relationship between
neocortex volume
•emotional closeness is the key parameter underlying the
hierarchical differentiation of social networks
•the various human groups that can be identified in any society
seem to cluster around a series of values representing different
degrees of familiarity. The size of these layers tends to increase
by a multiple of three (circles of acquaintanceship [1]).

Validation: Twitter Networks [6]
6 months, 380 million of tweets, 25 million conversations, 1.7
million individuals.
!
Network of conversations considering only active communications
from one user to another to discount occasional social interactions
!
When A follows B, A becomes one of B’s followers and B is one of
A’s friends.
!
Weighted edges were the weight is the number of times user i
replies to user j as a direct measurement of the interaction strength
(stable relations will have large weights)
!
Average social strength of active initiate relationship:
[6] Gonçalves, Bruno, Nicola Perra, and Alessandro Vespignani. "Modeling users'
activity on twitter networks: Validation of dunbar's number." PloS one 6.8 (2011):
e22656.

Validation: Twitter Networks
Remarks:
•maximum between 100 and 200 friends, and the number of
reciprocated connections (ρ) saturate.
•The behavior can be reproduced by agents with a fixed size queue
and reply priorities (represents finite cognitive and time
capabilities)

Impact of Social Medias [7]
Examine the relationships between use of social media (IM and
OSN), network size, and emotional closeness
!
Does Internet use have a positive or negative impact on the
number and quality of social relationships people can maintain with
others?
!
Cyberpessimists vs Cyberoptimists:
•Time is inelastic. Time spent on the Internet displaces time
spent on socializing and doing face-to-face activities
•Communication over the Internet tends to supplement, rather
than replace, other forms of communication
!
If maintaining relationships via IM/SNS is more temporally efficient
and cognitively effective than maintaining relationships using other
modes of communication, SNS use may allow for weak
relationships to be maintained at higher level of trust.
[7] Pollet, Thomas V., Sam GB Roberts, and Robin IM Dunbar. "Use of social network
sites and instant messaging does not lead to increased offline social network size, or
to emotionally closer relationships with offline network members." Cyberpsychology,
Behavior, and Social Networking 14.4 (2011): 253-258.

Impact of Social Medias
RQ1: Is use of instant messaging or social networking sites
associated with an increased offline and online social network size?
!
Instant Messaging:
•users of IM didn’t have statistically significant bigger offline
social network size
•no significant correlation between time spent on IM and online
social network size
•significant correlation between time spent on IM and the
number of individuals contacted online weekly
!
Social Networking Sites:
•users of SNS didn’t have statistically significant bigger offline
social network size
•significant correlation between time spent on SNS and online
network size
•significant correlation between time spent on SNS and number
of weekly online contacts

RQ2: Is use of instant messaging or social networking sites
associated with an increase in average emotional closeness to
offline network members?
!
•no associations between using IM or SNS and closeness with
sympathy group
!
•the amount of time spent on IM did not correlate with
emotional closeness at any network layer

Remarks:
•time spent using social media is associated with a larger number
of online social network “friends”
•time spent using social media is not associated with larger offline
networks
•time spent using social media is not associated to feeling
emotionally closer to offline network members
•users of social media don’t have larger offline networks, and they
aren’t emotionally closer to offline network members
!
Social media use does not relax the time and cognitive constraints
on offline network size. Time is inelastic and there is a limited
amount of leisure time in any given day.

Social Implications: Beating Dunbar’s Number [8]
If Dunbar’s number is all people can manage it might become
important for you to ensure that you are part of people’s 150.
!
Connect with those who are cultivating powerful networks of their
own (e.g., geographically, vertically)
!
Be at the Elbow of Every Deal. If you have some value to offer,
people seek you out.
!
Keep a Pulse In Between Contacts. Use social networks to keep a
live pulse information moving along.
[8] Beating Dunbar’s Number:
http://www.chrisbrogan.com/beating-dunbars-number/

Social Implications: The Strength of Weak Ties [9]
Real value of collaboration and of networks doesn’t come from
strong relationships and networks but from weak one’s
!
Weak ties form bridges to different networks, while strong ties
tend to be inside of our own network
!
Weak ties are good because they take less time
!
Social networks allow us to build massive networks of weak ties
[9] Why Dunbar's Number is Irrelevant:
http://socialmediatoday.com/index.php?q=SMC/169132

Social Implications: Community Over ‘Friends’ [1, 2]
The 150 limit was developed at a time when people lived geographically
close. In small-scale communities there is almost complete overlap in
people’s social networks
!
The trends toward urbanization and economic migration changed that.
At each step we leave behind small groups of friends until time and
distance eventually dim the relationships with them
!
The effect is that today people’s network is fragmented, consisting of
small lusters of friends, and clusters rarely overlap — it’s much harder
to keep relationships working when they are distributed
!
Fragmented and geographically distributed social networks means that
there is less to bind us to the fabric of local communities. Relationships
involved across big units become very casual (no sense of obligation,
reciprocity, and trust), thus peer pressure, which is usually sufficient to
police everyone’s behavior, is very small.
!
The fragmentation may be part of the reason why modern urban
societies seem to be so dysfunctional.
!
Create a greater sense of community (e.g., religion? meh…)

Conclusion
“Friends, if you don’t see them, will gradually
cease to be interested in you.
!
Family relationships instead seem to be very
stable. No matter how far away you go, they
love you when you come back.”
!
Robin I. M. Dunbar

CSE5656 Complex Networks - Dunbar's Number

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