2. ABSTRACT
 Stability and evolution of networks
 Partner and environment
 Social network formation – ABM – CAs
 Emergence of consensus
 Impulsive = strong ties
 Structural hole, local influence

3. OBJECTIVES
 Analyze the use of cellular automata (CAs) in
modeling the dynamic process of partner
selection in business network formation in
the dentistry context
– secondary goal was to verify the influence of
interactions among the dentists in the network
dynamics.

4. VARIABLES
 Redirection of a patient with special needs,
beyond a particular dentist’s expertise, to
another dentist of the network
 Patient better served
 Choices build a social network

5. SOCIAL NETWORKS AS COMPLEX
SYSTEMS
 Dissemination and use of information in a
social system = complex adaptive system
 Individuals → interact (non trivial way) →
visible collective behavior → emergent
phenomena

6. AGENT-BASED MODELING
 Agents are autonomous, interdependent, follow
simple rules, are adaptive and consider the past
 Differs from prior use of computation in sociology →
considers interactions, instead of simply proposing
algorithms and equations to represent behavioral
processes.
 Not oriented to the goal, but to the emergence of
phenomena → more freedom and space for
randomness and “unexpected” results → build theory

7. CELLULAR AUTOMATA
 Fully discrete, complex systems that possess
both a dynamic and a computational nature
 Grid-like regular lattice of cells, and a state
transition rule (uniform)
 Local connections to other cells, boundary
condition, usually periodic

9. Network rationale
Partner selection
Interaction
Convergence of
partner selection
criteria
Stronger ties
More impulsiveness
H3
H5
Different rationale
Structural hole
Increases distance
Impulsiveness
H2
Local influence
H1
H4
HYPOTHESES

10. VARIABLES
 Strength of ties = N of clients indicated in a week x
how long these indications occurred + number of
clients received in a week x how long the clients
have been received.
 Business scope = N specialties offered + number of
employees + number of work days in the week +
number of clients treated in a day
 Partner selection = reputation, proximity, expected
quality, financial aspects, resources complementary

11. VARIABLES
 Impulsiveness = time spent to analyze the
situation, level of emotion in the decision,
degree of risk aversion, planning time and
degree of qualitative and quantitative
analysis of the benefits
 Leadership = moderating variable =
perception on the leadership characteristics
of the partner

12. DATA COLLECTION
 Regional Council of Dentistry database (CROSP)
 Likert 1 to 6
 Pre test 30 individuals
 Snow-ball type (e-mails)
 Randomly selected sample from the database,
composed by 2200 letters and 960 emails.
 313 dentists
 4 questionnaires excluded → missing values
 18 small amount of missing values → average
 4 outliers – model with and without them

13. DATA PROCESSING
 Factorial analysis – Varimax rotation – 10 factors
 Discriminant validity
 Ordered following leadership
 Factor values transformed into a single scale, from 0 to
255. For every factor, a distance measure was
computed (Di0) between every (ith) individual and the
pivot
)( 0
10
1
0 n
n
nii XXD ∑=
−=

14. DATA PROCESSING
 Threshold scale was used to transform the decimal
factor values into binary representation
 N of classes = Sturge’s rule
 C=1+3.332*Log10N
 Each factor value was then converted to 9-bit-long
binary number, following the threshold scale
 associating bit 1 to the position corresponding to the
interval containing the value

15. Limite Limite
22,1 95,4 14,9 43,3 Inferior Superior
1 0 1 0 0,000 28,333
0 0 0 1 28,333 56,667
0 0 0 0 56,667 85,000
0 1 0 0 85,000 113,333
0 0 0 0 113,333 141,667
0 0 0 0 141,667 170,000
0 0 0 0 170,000 198,333
0 0 0 0 198,333 226,667
0 0 0 0 226,667 255,000
300 301 302 303Individual
Distance
Lower
limit
Upper
Limit
9 ECAs
(303 i)
DATA PROCESSING

16. DATA PROCESSING
 Rule:
– allow more than 10 iterations
– convergence to a fixed point and not a cyclic
attractor in less than 308 iterations
– its transient would not be too long
 Chosen rule: 234 out of the 256 possible
ECA rules

17. RULE 234
 Individual’s opinion follows the local majority, but if the individual
does not consider the specific partner selection criteria as
relevant the same way the most influent neighbour (i.e., the one in
the leftmost position) does, that is, both of them have value 0 to
that partner selection criteria, the individual changes its original
opinion and turns it to the same as the least influent neighbour

18. DATA PROCESSING
 Stop criterion = fixed point or 308 iteractions
– transitivity
 Each column back to decimal

20. RESULTS
 In the modeling phase each rule generated a
different special positioning, thus confirming
hypothesis H4
 Initial distances great variation (range -250 to 250) =
different selection criteria. After rule 234 application
reduction to a range of 0.08 = individuals get closer
to each other, due to tie strengthening and an
increase in the degree of similarity, confirming H3 and
H5

21. RESULTS
Evolução das discrepâncias individuais
0
10
20
30
40
50
60
70
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301
Indivíduos
Discrepânciasindividuais
Threshold26º cycle
Quality

22. RESULTS
Distâncias nos momentos inicial e final após 308 ciclos
-250
-200
-150
-100
-50
0
50
100
150
200
250
-46 4 54 104 154 204 254 304
Indivíduos
Distâncias
DISTANCE
INDIVIDUALS
CONSENSUS

23. RESULTS
 Individual 249 different rationale
 less impulsive individual, very rational and
with low cooperation propensity

24. RESULTS
Distâncias finais após 308 ciclos
238
261
249
-0,02
-0,01
0
0,01
0,02
0,03
0,04
0,05
0,06
0 50 100 150 200 250 300
Indivíduos
Distâncias
DISTANCE
INDIVIDUALS

25. RESULTS
-0,02
-0,01
0
0,01
0,02
0,03
0,04
0,05
0,06
0 50 100 150 200 250 300 350
Indivíduos
Distânciasfinais
Internal
weak tie
DISTANCE
INDIVIDUALS

26. RESULTS
 The increase in tie strength caused an
increase in impulsiveness and a greater
cooperation propensity, because there was
the same rationality in the network
 Behavior reinforcements

27. RESULTS
 The insertion of a structural hole using rule
204 in the 150th individual, that is, an
individual that did not change its opinions
along the interactions, moved away
individuals from the 45th to the 150th, who
formed a cluster. Local Influence
 Confirming H1, H2 and H6

28. RESULTS
Efeitos de um buraco estrutural no 150º indivíduo no ciclo 308
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 50 100 150 200 250 300 350
Indivíduos
Distâncias
DISTANCE
INDIVIDUALS
STRUCTURAL HOLE

30. CONCLUSIONS
 study contributes to theory insofar as it allowed to
verify the potential use of cellular automata to
understand formation and evolution of social
networks
 Emergent phenomena suggests a dynamic partner
selection decision criteria classification and allows to
understand the formation of weak ties as well as the
emergence of consensus in the network