1) Theoretical physics theories are more valid if they can predict new phenomena that can be tested, rather than just explaining existing phenomena. 2) The document presents three examples from network science that demonstrate both explanation and prediction: (i) predicting epidemic spreading, (ii) predicting abrupt breakdown of interconnected networks, and (iii) predicting El Niño events. 3) Research on coupled networks found that the robustness of interconnected networks decreases abruptly rather than continuously as networks become more complex, moving from a second-order transition to a first-order transition with cascading failures.

1. SHLOMO HAVLIN
Bar-Ilan University
Explain or Predict
1. Explaining and understanding a physical phenomena
usually leads to predictions:
Examples: the Higgs Boson, photo electric ….
2. Theory without predictions of new phenomena and
the possibility of testing the predictions is
usually not regarded as a valid theory!
3. I will present three examples from my current field:
(i) Early predicting of epidemic spreading
(ii) Abrupt breakdown of a system of systems
represented as “network of networks”
(iii) Early prediction of El-Nino events (Unpublished)
Explain AND Predict

2. Based on theoretical paper of Cohen, Havlin and ben-Avraham, PRL 91, 247901 (2003)

4. Single and coupled networks: Robustness
ER
Remove randomly (or targeted) a
fraction 1 − p nodes
P∞ Size of the largest
connected component (cluster)
pc Breakdown threshold
Giant component and breakdown
thresholds are predicted 1
Single ER
for these models
P∞ = p[1 − exp(− k P∞ )] Coupled
P∞
Single networks:
Continuous abrupt
Continuous transition
Cascades,
Sudden
Coupled networks: breakdown
New paradigm-Abrupt transition 0
0 pc p pc 1
Cascading Failures

5. Network of Networks (tree)
n=5
For ER, ki = k full coupling ,
ALL loopless topologies (chain, star, tree):
P∞ = p[1 − exp(− k P∞ )] n
P∞
n=1 known ER- 2nd order
n=1
n=5
pc = 1/ k
n=2
Vulnerability increases significantly with n Buldyrev et al Nature (2010)
Gao et al PRL (2011)