Embed Size (px)
Citation preview
Comparative Study of Network Robustness of Different Complex
Network Models subjected to Edge-Attack
Ankit Upadhyay 2011020 Laxman Sharma 2011072 Pranjal Nautiyal 2011104 Praveen Kumar 2011107 Ashish Panchal 2011205
ES 306b: Complex Network Project
Project Overview
• Study of impact of edge attack on network robustness• We analysed the impact of edge attack on ER and WS
complex models• Robustness of these 2 models were compared with each
other, subject to multiple edge attacks
ER Model: - Vertices are connected by randomly chosen edges, without any bias- Poisson-type degree distribution
WS model- Regular Network is re-wired, forming a short cut- Power law distribution is followed
Network Robustness- Attack vulnerablitiy denotes the degree to which network performance decreases due to edge attack.- Network Resilience is the extent to which network remains unaffected by edge and vertex attack
FUNFAMENTAL THEORY & CONCEPTS
CONCEPT USED
- Average path length of network is an important
measure of network robustness.- Removal of edges causes decrease in path length- The model in which decrease in path length is more dramatic is weaker/ less robust
STRATEGY USED
- We began with adjacency matrices of both WS and ER models of complex network- Then the edges were attacked and removed one by one- Average path length was evaluated after each edge attack and compared for both the
models
Implementation
• MATLAB codes were written for evaluation of average degree and edge removal for both ER & WS models
• Graphs were plotted corresponding to both the models, after each attack
• We considered 8 node network for both the models (for the sake of analysis & understanding)
ER Model of Random Network
W = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ];A = [6 1 2 2 3 4 4 5 5 6 1 1 7 8 6 7 ];B = [2 6 3 5 4 1 6 3 4 3 5 7 2 5 8 8 ];DG = sparse(A,B,W)sum = 0;UG = tril(DG + DG');h = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist,path,pred] = graphshortestpath(UG,i,j,'directed',false) sum = sum+dist; endendavg = sum/56;
W1 = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ];A1 = [1 2 2 3 4 4 5 5 6 1 1 7 8 6 7 ];B1 = [6 3 5 4 1 6 3 4 3 5 7 2 5 8 8 ];DG = sparse(A1,B1,W1)sum1 = 0;UG = tril(DG + DG');h1 = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist1,path1,pred1] = graphshortestpath(UG,i,j,'directed',false) sum1 = sum1+dist1; endendavg1 = sum1/56;
W2= [1 1 1 1 1 1 1 1 1 1 1 1 1 1 ];A2 = [2 2 3 4 4 5 5 6 1 1 7 8 6 7 ];B2 = [3 5 4 1 6 3 4 3 5 7 2 5 8 8 ];DG = sparse(A2,B2,W2)sum2 = 0;UG = tril(DG + DG');h2 = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist2,path2,pred2] = graphshortestpath(UG,i,j,'directed',false) sum2 = sum2+dist2; endendavg2 = sum2/56;
W3= [1 1 1 1 1 1 1 1 1 1 1 1 1 ];A3 = [2 3 4 4 5 5 6 1 1 7 8 6 7 ];B3 = [5 4 1 6 3 4 3 5 7 2 5 8 8 ];DG = sparse(A3,B3,W3)sum3 = 0;UG = tril(DG + DG');h3 = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist3,path3,pred3] = graphshortestpath(UG,i,j,'directed',false) sum3 = sum3+dist3; endendavg3 = sum3/56;
WS Model of small world networkW = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1];A = [ 1 1 1 1 2 2 2 3 3 4 4 5 5 5 6 8];B = [ 2 3 6 8 3 4 8 4 7 5 6 6 7 8 7 7];DG = sparse(A,B,W)sum = 0;UG = tril(DG + DG');h = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist,path,pred] = graphshortestpath(UG,i,j,'directed',false) sum = sum+dist; endendavg = sum/56;
W1 = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1];A1 = [ 1 1 1 2 2 2 3 3 4 4 5 5 5 6 8];B1 = [ 3 6 8 3 4 8 4 7 5 6 6 7 8 7 7];DG = sparse(A1,B1,W1)sum1 = 0;UG = tril(DG + DG');h1 = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist1,path1,pred1] = graphshortestpath(UG,i,j,'directed',false) sum1 = sum1+dist1; endendavg1 = sum1/56;
W2 = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1];A2 = [ 1 1 2 2 2 3 3 4 4 5 5 5 6 8];B2 = [ 6 8 3 4 8 4 7 5 6 6 7 8 7 7];DG = sparse(A2,B2,W2)sum2 = 0;UG = tril(DG + DG');h2 = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist2,path2,pred2] = graphshortestpath(UG,i,j,'directed',false) sum2 = sum2+dist2; endendavg2 = sum2/56;
W3 = [1 1 1 1 1 1 1 1 1 1 1 1 1];A3 = [1 2 2 2 3 3 4 4 5 5 5 6 8];B3 = [8 3 4 8 4 7 5 6 6 7 8 7 7];DG = sparse(A3,B3,W3)sum3 = 0;UG = tril(DG + DG');h3 = view(biograph(UG,[],'ShowArrows','off','ShowWeights','on'))for i = 1:8 for j = 1:8 [dist3,path3,pred3] = graphshortestpath(UG,i,j,'directed',false) sum3 = sum3+dist3; endendavg3 = sum3/56;
RESULTS
Initially: Average Path length = 1.4286
After removing 1 edge: Average Path length = 1.4643
After removing 2 edges: Average Path length = 1.5000
ER Model
WS Model
Initially: Average Path length = 1.4286
After removing 1 edge: Average Path length = 1.4643
After removing 2 edges: Average Path length = 1.5357
CONCLUSION
• As the edges are removes, the average path length of the network increases, signifying a decrease in its robustness
• The increase in average path length is more pronounced for WS network that ER, suggesting that ER model is more robust than WS.
THANK YOU
