1. Topics on Influence Processes
Large Networks 2004, UCL

2. In short… The Influence Model The Voter Model
Spread of Infectious Diseases
Interests
General vision
Similarity between Graph Vertices

3. The Influence Model dangerous stressed irritated relax irritated
1/2
1/3
1/6
irritated
relax
irritated
stressed
dangerous
1/10
3/10
4/10
2/10

4. The Influence Model Homogeneous Model: same influence
Binary Model: 2 states, imitating

5. The Voter Model
- Symmetric
- Absorbing state
- p[1] and p[2]

6. The Voter Model

7. The Voter Model
(.35,0)
interface

8. The Voter Model
(.27,0)
interface

9. The Voter Model
(.31,0)
interface

10. The Voter Model
(.31,0)
uniform

11. Infectious Diseases M Reproduction number R0 S E I R deaths births
SIR: influenza
SIS: cold

12. Infectious Diseases
mixed
structured
bond percolation

13. Interests (1) Figure out catastrophes waves
Figure out opinion formation
Figure out phase transition
Relation with topology

14. Interests (2) Control catastrophes waves (to connect ?)
Control opinion formation (media)
Control spread of diseases (vaccinations)
Control phase transition (topology)

15. General Vision Time Discrete Continuous k l j i State Discrete
Function
Depends on I,j,k,l
Linear or Non-Linear
Stochastic or Deterministic
Depends on time
Different for subsets of nodes

16. Similarity between graph vertices1 2
Hub and Authority 1 2 3
+ intermediate node
(1,1,1)
(1,1,0)
(2,2,0)
(1,1,1)
(0,2,2) a a
(0,2,2) a c c c b b b
(1,1,1)
(1,1,0)
(2,2,0)
(2,2,0)
(4,4,0)
(0,4,4)
(0,4,4) a a c c b b
(2,2,0)
(4,4,0)