Presentation nipun puri
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Using Different method to describe the centrality in a network
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Presentation nipun puri
- 1. Using Shortest Path problem to study social networks nipun
- 3. HOW DOES A DISEASE SPREAD IN A NETWORK?
- 5. Simulation pseudo-code infect a random person for neighbor in neighbours: rand = randBetween(0,1):#uniform if (rand <= .30): infect the person elseif(rand > .30): do not infect the person
- 6. Number of people with the disease Frequency Probability of contacting the disease .30 Number of simulations 1000 Average # sick patients 42/350 Simulating the spread of a disease in a network
- 7. VACCINATION How to stop the disease from spreading?
- 8. RANDOM VACCINATION How to stop the disease from spreading?
- 9. Simulation pseudo-code remove n random people from the network infect a random person for neighbor in neighbours: rand = randBetween(0,1):#uniform if (rand <= .30): infect the person elseif(rand > .30): do not infect the person
- 10. Number of people with the disease Frequency Probability of contacting the disease .30 Number of simulations 1000 Average # sick patients 33/350 # of vaccinations 50 Simulating the spread of a disease in a network – random vaccination This was 300 in the previous histogram. Nothing in the range 90-100
- 11. VACCINATE THE MORE CENTRAL NODES How to stop the disease from spreading?
- 12. Measures of centrality of a node 1. Closeness Centrality 2. Clustering coefficient 3. Degree
- 13. Closeness Centrality • Closeness centrality of the node = Sum of the lengths of the shortest path from one node to all the other nodes
- 14. How to find the shortest path? • In an undirected graph where all the nodes are equidistant (all distances = 1) • Breadth first search
- 16. 1. Start with Beth
- 17. 2. Distance between Beth and her immediate neighbor is 1
- 18. 3. Distance between their immediate neighbor and Beth is two
- 19. 4. Distance between their immediate neighbor and Beth is three Closeness centrality is the sum of all these numbers Beth’s closeness centrality is 24
- 20. Simulation pseudo-code remove n closest people from network infect a random person for neighbor in neighbours: rand = randBetween(0,1):#uniform if (rand <= .30): infect the person elseif(rand > .30): do not infect the person
- 21. Number of people with the disease Frequency Random vaccination Closeness centrality Probability of contacting the disease .30 .30 Number of simulations 1000 1000 Average # sick patients 33 13 # of vaccinations 50 50 Simulating the spread of a disease in a network – closeness centrality This was 350 in the random vaccination case Nothing in the range 70-100!
- 22. Measures of centrality in a network 1. Closeness Centrality 2. Clustering coefficient 3. Degree
- 23. Clustered vs. non clustered graph
- 24. .192/3 = .67 Local clustering coefficient of a node number of links between its neighbors total number of possible links Remove nodes with a low clustering coefficient = n*(n-1)/2
- 25. Bigger size corresponds to a larger clustering coefficient I want to vaccinate nodes with a small clustering coefficient These hold the network together
- 26. Number of people with the disease Frequency Random vaccination Closeness centrality Clustering coefficient Probability of contacting the disease .30 .30 .30 Number of simulations 1000 1000 1000 Average # sick patients 33 13 41 # of vaccinations 50 50 50 Simulating the spread of a disease in a network – clustering coefficient This was 350 in the random vaccination case Even worse than random vaccination!
- 27. Measures of centrality in a network 1. Closeness Centrality 2. Clustering coefficient 3. Degree
- 30. Simulation pseudo-code remove n people with the highest degree infect a random person for neighbor in neighbours: rand = randBetween(0,1):#uniform if (rand <= .30): infect the person elseif(rand > .30): do not infect the person
- 31. Number of people with the disease Frequency Random Closeness centrality Clustering coefficient Degree Probability .30 .30 .30 .30 Number of simulations 1000 1000 1000 1000 Average # sick patients 33 13 41 11 # of vaccinations 50 50 50 50 Simulating the spread of a disease in a network – degree Looks like a negative exponential distribution Simplest method with best results
- 32. Summary • Studying social networks which have a special property that the all the distances are one • BFS : Shortest Path Problem • Clustering Co-efficient of a node • Degree of a node. Best results!
- 33. Resources
Hinweis der Redaktion
- Explain the histogram
- This graph has on an average a high clustering co-efficient. Which means that there are concentrated clusters. But, there are a few, like node #5, with a low clustering co-efficient which is helping the whole network stay in touch.