Siddhartha Gunda Sorabh Hamirwasia Generating small world network model. Optimal network property for decentralized search. Variation in epidemic dynamics with structure of network. What is small world network model ? Watts-Strogatz vs Kleinbergs Model. BFS vs Decentralized search. 2D latticeKleinbergs Model Step 1- Select source and target node randomly. Step 2 Send message using decentralized search. At each node find neighbor nearest to the target. Pass message to the neighbor found above. Repeat till message reaches target node. Compute hops required. Step 3 - Repeat Step1and Step2 for N cycles. Step 4 - Calculate average number of hops. Parameters: Lattice dimension = 2, Number of Nodes/dimension = 100, Number of iterations = For same value of r, decrease in q results in increase in average path length. For different values of r, optimal average length is found at r = 2. Epidemic Models. Branching Model. SIS Model SIR Model SIRS Model SIRS over SIR Step 1 Generate Kleinbergs graph. Step 2 Simulate SIRS algorithm. If state = Susceptible Check if node can get infection. If yes change the state to infected. If state = Infected Check if T I expires. If yes change the state to recovery. If state = Recovered Check if T R expires. If yes change the state to susceptible. Step 3 Store number of infected nodes. Step 4 Repeat above steps for N cycles. 1000 Cycles r=0 means uniform probability. Behavior same as Watts-Strogatz Model. For constant q, Decrease in r results in increase in p for same distance. Hence high synchronization. For constant r, Decrease in q results in decrease in p. Hence low synchronization. [1] Jon Kleinberg. The small-world phenomenon: an algorithmic perspective. In Proc.32nd ACM Symposium on Theory of Computing, pages 163170, [2] Marcelo Kuperman and Guillermo Abramson. Small world effect in an epidemiological model. Physical Review Letters, 86(13):2909 2912, March 2001. Questions ? Thank You!