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Complex Networks: Design Philosophy and Analyses

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Complex Networks: Design Philosophy and Analyses

  1. 1. Outline Introduction Topological Features Philosophy Design Analyses Conclusions An Overview of Complex Networks Design and Analyses Sanket Patil May 12, 2008 Sanket Patil An Overview of Complex Networks Design and Analyses
  2. 2. Outline Introduction Topological Features Philosophy Design Analyses Conclusions 1 Introduction Definition Representation 2 Topological Features Scale-free Nature “Small World” properties Other features 3 Philosophy Emergence Machines vs Societies Self Interest 4 Design Systems Design: Desiderata Complex Systems Design 5 Analyses 6 Conclusions Sanket Patil An Overview of Complex Networks Design and Analyses
  3. 3. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Complex Networks Not “simple networks” Not random graphs Have non-trivial topological features Sanket Patil An Overview of Complex Networks Design and Analyses
  4. 4. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Complex Networks Not “simple networks” Not random graphs Have non-trivial topological features Sanket Patil An Overview of Complex Networks Design and Analyses
  5. 5. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Complex Networks Not “simple networks” Not random graphs Have non-trivial topological features Sanket Patil An Overview of Complex Networks Design and Analyses
  6. 6. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Examples Computer Networks, the Internet, the Web Food-webs, protein interaction networks Social Networks, Trade Networks The brain Sanket Patil An Overview of Complex Networks Design and Analyses
  7. 7. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Examples Computer Networks, the Internet, the Web Food-webs, protein interaction networks Social Networks, Trade Networks The brain Sanket Patil An Overview of Complex Networks Design and Analyses
  8. 8. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Examples Computer Networks, the Internet, the Web Food-webs, protein interaction networks Social Networks, Trade Networks The brain Sanket Patil An Overview of Complex Networks Design and Analyses
  9. 9. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Examples Computer Networks, the Internet, the Web Food-webs, protein interaction networks Social Networks, Trade Networks The brain Sanket Patil An Overview of Complex Networks Design and Analyses
  10. 10. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Complex Networks Designed (for performance) Have evolved/emerged over time Are teleological / have purpose of life Sanket Patil An Overview of Complex Networks Design and Analyses
  11. 11. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Complex Networks Designed (for performance) Have evolved/emerged over time Are teleological / have purpose of life Sanket Patil An Overview of Complex Networks Design and Analyses
  12. 12. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Complex Networks Designed (for performance) Have evolved/emerged over time Are teleological / have purpose of life Sanket Patil An Overview of Complex Networks Design and Analyses
  13. 13. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Representation Networks are modelled as “Graphs” A node/vertex/point represents a machine, a human, a cell etc. An edge/arc/line represents a relation between two nodes Edges can be undirected or directed. Weights are used to convey additional (extra-topological) information Sanket Patil An Overview of Complex Networks Design and Analyses
  14. 14. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Basic Definitions Degree: The number of edges incident on a node Indegree (outdegree): Number of incoming (outgoing) edges Degree Distribution: A probability distribution of node degrees Sanket Patil An Overview of Complex Networks Design and Analyses
  15. 15. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Basic Definitions Degree: The number of edges incident on a node Indegree (outdegree): Number of incoming (outgoing) edges Degree Distribution: A probability distribution of node degrees Sanket Patil An Overview of Complex Networks Design and Analyses
  16. 16. Outline Introduction Topological Features Definition Philosophy Representation Design Analyses Conclusions Path: A sequence of adjacent vertices Pathlength: The number of edges in a path Sanket Patil An Overview of Complex Networks Design and Analyses
  17. 17. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Scale-free Nature Network dynamics/behaviour is independent of the size Power Law degree distributions Sanket Patil An Overview of Complex Networks Design and Analyses
  18. 18. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Scale-free Nature Network dynamics/behaviour is independent of the size Power Law degree distributions Sanket Patil An Overview of Complex Networks Design and Analyses
  19. 19. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Power Law Distribution Sanket Patil An Overview of Complex Networks Design and Analyses
  20. 20. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Properties P[X = k] α k −p Small number of nodes with a very high degree and a large number of nodes with a very low degree “heavy tail”, “long tail”, “80:20” Income distributions, page rank, wikipedia contribution Sanket Patil An Overview of Complex Networks Design and Analyses
  21. 21. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Properties P[X = k] α k −p Small number of nodes with a very high degree and a large number of nodes with a very low degree “heavy tail”, “long tail”, “80:20” Income distributions, page rank, wikipedia contribution Sanket Patil An Overview of Complex Networks Design and Analyses
  22. 22. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Properties P[X = k] α k −p Small number of nodes with a very high degree and a large number of nodes with a very low degree “heavy tail”, “long tail”, “80:20” Income distributions, page rank, wikipedia contribution Sanket Patil An Overview of Complex Networks Design and Analyses
  23. 23. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Properties P[X = k] α k −p Small number of nodes with a very high degree and a large number of nodes with a very low degree “heavy tail”, “long tail”, “80:20” Income distributions, page rank, wikipedia contribution Sanket Patil An Overview of Complex Networks Design and Analyses
  24. 24. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Preferential Attachment Nodes prefer to attach to “popular” nodes “Rich getting richer” Entrenchment Sanket Patil An Overview of Complex Networks Design and Analyses
  25. 25. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Preferential Attachment Nodes prefer to attach to “popular” nodes “Rich getting richer” Entrenchment Sanket Patil An Overview of Complex Networks Design and Analyses
  26. 26. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Preferential Attachment Nodes prefer to attach to “popular” nodes “Rich getting richer” Entrenchment Sanket Patil An Overview of Complex Networks Design and Analyses
  27. 27. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions “Small World” Properties Stanley Milgram: Small world experiment Mean Path Length 6 Critique: not a comprehensive study “Six degrees of separation” Watts and Strogatz Sanket Patil An Overview of Complex Networks Design and Analyses
  28. 28. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions “Small World” Properties Stanley Milgram: Small world experiment Mean Path Length 6 Critique: not a comprehensive study “Six degrees of separation” Watts and Strogatz Sanket Patil An Overview of Complex Networks Design and Analyses
  29. 29. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions “Small World” Properties Stanley Milgram: Small world experiment Mean Path Length 6 Critique: not a comprehensive study “Six degrees of separation” Watts and Strogatz Sanket Patil An Overview of Complex Networks Design and Analyses
  30. 30. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions “Small World” Properties Stanley Milgram: Small world experiment Mean Path Length 6 Critique: not a comprehensive study “Six degrees of separation” Watts and Strogatz Sanket Patil An Overview of Complex Networks Design and Analyses
  31. 31. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions “Small World” Properties Stanley Milgram: Small world experiment Mean Path Length 6 Critique: not a comprehensive study “Six degrees of separation” Watts and Strogatz Sanket Patil An Overview of Complex Networks Design and Analyses
  32. 32. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Saul Steinberg: Ninth Avenue Sanket Patil An Overview of Complex Networks Design and Analyses
  33. 33. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Social Commentary Small world geometry Sanket Patil An Overview of Complex Networks Design and Analyses
  34. 34. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Social Commentary Small world geometry Sanket Patil An Overview of Complex Networks Design and Analyses
  35. 35. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Kleinberg’s “small world” Ninth Avenue as a powerful analogy The “far” is almost as accessible as the “near” How are your friends/acquaintances distributed? Sanket Patil An Overview of Complex Networks Design and Analyses
  36. 36. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Kleinberg’s “small world” Ninth Avenue as a powerful analogy The “far” is almost as accessible as the “near” How are your friends/acquaintances distributed? Sanket Patil An Overview of Complex Networks Design and Analyses
  37. 37. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Kleinberg’s “small world” Ninth Avenue as a powerful analogy The “far” is almost as accessible as the “near” How are your friends/acquaintances distributed? Sanket Patil An Overview of Complex Networks Design and Analyses
  38. 38. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Sanket Patil An Overview of Complex Networks Design and Analyses
  39. 39. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Coefficient Neighbourhood: Nodes that are adjacent to a node no of edges in the neighbourhood Ci = total possible edges n i=0 Ci Cgraph = n Sanket Patil An Overview of Complex Networks Design and Analyses
  40. 40. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Coefficient Neighbourhood: Nodes that are adjacent to a node no of edges in the neighbourhood Ci = total possible edges n i=0 Ci Cgraph = n Sanket Patil An Overview of Complex Networks Design and Analyses
  41. 41. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Coefficient Neighbourhood: Nodes that are adjacent to a node no of edges in the neighbourhood Ci = total possible edges n i=0 Ci Cgraph = n Sanket Patil An Overview of Complex Networks Design and Analyses
  42. 42. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Small Worlds High clustering coefficient Low average path length Sanket Patil An Overview of Complex Networks Design and Analyses
  43. 43. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Navigability in small worlds Kleinberg’s metric space models (circa 2000) Short paths do exist But can we find them using local information? Sanket Patil An Overview of Complex Networks Design and Analyses
  44. 44. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Navigability in small worlds Kleinberg’s metric space models (circa 2000) Short paths do exist But can we find them using local information? Sanket Patil An Overview of Complex Networks Design and Analyses
  45. 45. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Navigability in small worlds Kleinberg’s metric space models (circa 2000) Short paths do exist But can we find them using local information? Sanket Patil An Overview of Complex Networks Design and Analyses
  46. 46. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Short range and long range connections Sanket Patil An Overview of Complex Networks Design and Analyses
  47. 47. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Exponent Connections based on distance (r) and clustering exponent α For a node u, the probability of connecting to v is r −α Highly clustered neighbourhood Number of long range links decays with distance Only when α = 2, a decentralized routing algorithm can be found which has a log n bound Sanket Patil An Overview of Complex Networks Design and Analyses
  48. 48. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Exponent Connections based on distance (r) and clustering exponent α For a node u, the probability of connecting to v is r −α Highly clustered neighbourhood Number of long range links decays with distance Only when α = 2, a decentralized routing algorithm can be found which has a log n bound Sanket Patil An Overview of Complex Networks Design and Analyses
  49. 49. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Exponent Connections based on distance (r) and clustering exponent α For a node u, the probability of connecting to v is r −α Highly clustered neighbourhood Number of long range links decays with distance Only when α = 2, a decentralized routing algorithm can be found which has a log n bound Sanket Patil An Overview of Complex Networks Design and Analyses
  50. 50. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Exponent Connections based on distance (r) and clustering exponent α For a node u, the probability of connecting to v is r −α Highly clustered neighbourhood Number of long range links decays with distance Only when α = 2, a decentralized routing algorithm can be found which has a log n bound Sanket Patil An Overview of Complex Networks Design and Analyses
  51. 51. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Clustering Exponent Connections based on distance (r) and clustering exponent α For a node u, the probability of connecting to v is r −α Highly clustered neighbourhood Number of long range links decays with distance Only when α = 2, a decentralized routing algorithm can be found which has a log n bound Sanket Patil An Overview of Complex Networks Design and Analyses
  52. 52. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Finding short paths Sanket Patil An Overview of Complex Networks Design and Analyses
  53. 53. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Other Features Communities Hierarchical Structures Sanket Patil An Overview of Complex Networks Design and Analyses
  54. 54. Outline Introduction Topological Features Scale-free Nature Philosophy “Small World” properties Design Other features Analyses Conclusions Other Features Communities Hierarchical Structures Sanket Patil An Overview of Complex Networks Design and Analyses
  55. 55. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Complex Systems: Philosophy Systems Theory Cybernetics Non-linear Dynamics Multiagent Systems and AI Network Science, Connectionism, Cognitive Psychology Sanket Patil An Overview of Complex Networks Design and Analyses
  56. 56. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Complex Systems: Philosophy Systems Theory Cybernetics Non-linear Dynamics Multiagent Systems and AI Network Science, Connectionism, Cognitive Psychology Sanket Patil An Overview of Complex Networks Design and Analyses
  57. 57. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Complex Systems: Philosophy Systems Theory Cybernetics Non-linear Dynamics Multiagent Systems and AI Network Science, Connectionism, Cognitive Psychology Sanket Patil An Overview of Complex Networks Design and Analyses
  58. 58. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Complex Systems: Philosophy Systems Theory Cybernetics Non-linear Dynamics Multiagent Systems and AI Network Science, Connectionism, Cognitive Psychology Sanket Patil An Overview of Complex Networks Design and Analyses
  59. 59. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Complex Systems: Philosophy Systems Theory Cybernetics Non-linear Dynamics Multiagent Systems and AI Network Science, Connectionism, Cognitive Psychology Sanket Patil An Overview of Complex Networks Design and Analyses
  60. 60. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Strudy of Complex Networks Structure or Topology How structure governs the function How design can be analysed teleologically Can we use this knowledge to build better systems? Sanket Patil An Overview of Complex Networks Design and Analyses
  61. 61. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Strudy of Complex Networks Structure or Topology How structure governs the function How design can be analysed teleologically Can we use this knowledge to build better systems? Sanket Patil An Overview of Complex Networks Design and Analyses
  62. 62. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Strudy of Complex Networks Structure or Topology How structure governs the function How design can be analysed teleologically Can we use this knowledge to build better systems? Sanket Patil An Overview of Complex Networks Design and Analyses
  63. 63. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Strudy of Complex Networks Structure or Topology How structure governs the function How design can be analysed teleologically Can we use this knowledge to build better systems? Sanket Patil An Overview of Complex Networks Design and Analyses
  64. 64. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Emergence The connections between the components is as important as the components Emergent behaviour of complex networks Case Study: The Human Brain Sanket Patil An Overview of Complex Networks Design and Analyses
  65. 65. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Emergence The connections between the components is as important as the components Emergent behaviour of complex networks Case Study: The Human Brain Sanket Patil An Overview of Complex Networks Design and Analyses
  66. 66. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Emergence The connections between the components is as important as the components Emergent behaviour of complex networks Case Study: The Human Brain Sanket Patil An Overview of Complex Networks Design and Analyses
  67. 67. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Machines vs Societies Systems Thinking: parts and whole Machines funcion based on norms Societies are declarative Societies are more robust Case study: The Heart Sanket Patil An Overview of Complex Networks Design and Analyses
  68. 68. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Machines vs Societies Systems Thinking: parts and whole Machines funcion based on norms Societies are declarative Societies are more robust Case study: The Heart Sanket Patil An Overview of Complex Networks Design and Analyses
  69. 69. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Machines vs Societies Systems Thinking: parts and whole Machines funcion based on norms Societies are declarative Societies are more robust Case study: The Heart Sanket Patil An Overview of Complex Networks Design and Analyses
  70. 70. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Machines vs Societies Systems Thinking: parts and whole Machines funcion based on norms Societies are declarative Societies are more robust Case study: The Heart Sanket Patil An Overview of Complex Networks Design and Analyses
  71. 71. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Machines vs Societies Systems Thinking: parts and whole Machines funcion based on norms Societies are declarative Societies are more robust Case study: The Heart Sanket Patil An Overview of Complex Networks Design and Analyses
  72. 72. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Self Interest Autonomous agents Local constraints and self interest Global or environmental dampeners Sanket Patil An Overview of Complex Networks Design and Analyses
  73. 73. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Self Interest Autonomous agents Local constraints and self interest Global or environmental dampeners Sanket Patil An Overview of Complex Networks Design and Analyses
  74. 74. Outline Introduction Topological Features Emergence Philosophy Machines vs Societies Design Self Interest Analyses Conclusions Self Interest Autonomous agents Local constraints and self interest Global or environmental dampeners Sanket Patil An Overview of Complex Networks Design and Analyses
  75. 75. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Systems Design: Desiderata Safety Resilience Fairness Livenss Sanket Patil An Overview of Complex Networks Design and Analyses
  76. 76. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Systems Design: Desiderata Safety Resilience Fairness Livenss Sanket Patil An Overview of Complex Networks Design and Analyses
  77. 77. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Systems Design: Desiderata Safety Resilience Fairness Livenss Sanket Patil An Overview of Complex Networks Design and Analyses
  78. 78. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Systems Design: Desiderata Safety Resilience Fairness Livenss Sanket Patil An Overview of Complex Networks Design and Analyses
  79. 79. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Complex Systems Design Efficiency Robustness Cost Sanket Patil An Overview of Complex Networks Design and Analyses
  80. 80. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Complex Systems Design Efficiency Robustness Cost Sanket Patil An Overview of Complex Networks Design and Analyses
  81. 81. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Complex Systems Design Efficiency Robustness Cost Sanket Patil An Overview of Complex Networks Design and Analyses
  82. 82. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions An Optimization Problem Designing complex systems is an optmization process Search in a multidimensional space Sanket Patil An Overview of Complex Networks Design and Analyses
  83. 83. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions An Optimization Problem Designing complex systems is an optmization process Search in a multidimensional space Sanket Patil An Overview of Complex Networks Design and Analyses
  84. 84. Outline Introduction Topological Features Systems Design: Desiderata Philosophy Complex Systems Design Design Analyses Conclusions Approaches Mathematical Programming Ant Colony Optimization Swarm Intelligence Simulated Annealing Genetic Algorithms Sanket Patil An Overview of Complex Networks Design and Analyses
  85. 85. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Graph Theoretic Analyses Graph thoretic properties used in design and analyses Constraints and objectives are defined in terms of graph properties Design is usually evolution of optimal graphs under the given constraints Sanket Patil An Overview of Complex Networks Design and Analyses
  86. 86. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Graph Theoretic Analyses Graph thoretic properties used in design and analyses Constraints and objectives are defined in terms of graph properties Design is usually evolution of optimal graphs under the given constraints Sanket Patil An Overview of Complex Networks Design and Analyses
  87. 87. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Graph Theoretic Analyses Graph thoretic properties used in design and analyses Constraints and objectives are defined in terms of graph properties Design is usually evolution of optimal graphs under the given constraints Sanket Patil An Overview of Complex Networks Design and Analyses
  88. 88. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Efficiency APL: Average of all pairs shortest paths Diameter: The longest shortest path. An upper bound on efficiency. Sanket Patil An Overview of Complex Networks Design and Analyses
  89. 89. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Efficiency APL: Average of all pairs shortest paths Diameter: The longest shortest path. An upper bound on efficiency. Sanket Patil An Overview of Complex Networks Design and Analyses
  90. 90. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Local Objectives Eccentricity: The longest shortest path for a node The greatest separation a node suffers Average eccentricity or eccentricity distribution are also good indicators of efficiency Radius: Smallest eccentricity. “Central” node Number of “central” nodes can be another measure Sanket Patil An Overview of Complex Networks Design and Analyses
  91. 91. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Local Objectives Eccentricity: The longest shortest path for a node The greatest separation a node suffers Average eccentricity or eccentricity distribution are also good indicators of efficiency Radius: Smallest eccentricity. “Central” node Number of “central” nodes can be another measure Sanket Patil An Overview of Complex Networks Design and Analyses
  92. 92. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Local Objectives Eccentricity: The longest shortest path for a node The greatest separation a node suffers Average eccentricity or eccentricity distribution are also good indicators of efficiency Radius: Smallest eccentricity. “Central” node Number of “central” nodes can be another measure Sanket Patil An Overview of Complex Networks Design and Analyses
  93. 93. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Local Objectives Eccentricity: The longest shortest path for a node The greatest separation a node suffers Average eccentricity or eccentricity distribution are also good indicators of efficiency Radius: Smallest eccentricity. “Central” node Number of “central” nodes can be another measure Sanket Patil An Overview of Complex Networks Design and Analyses
  94. 94. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Local Objectives Eccentricity: The longest shortest path for a node The greatest separation a node suffers Average eccentricity or eccentricity distribution are also good indicators of efficiency Radius: Smallest eccentricity. “Central” node Number of “central” nodes can be another measure Sanket Patil An Overview of Complex Networks Design and Analyses
  95. 95. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Cost Density(connectance): no of edges/no of possible edges Edges per node Weights, costs and other environment dependent measures Sanket Patil An Overview of Complex Networks Design and Analyses
  96. 96. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Cost Density(connectance): no of edges/no of possible edges Edges per node Weights, costs and other environment dependent measures Sanket Patil An Overview of Complex Networks Design and Analyses
  97. 97. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Cost Density(connectance): no of edges/no of possible edges Edges per node Weights, costs and other environment dependent measures Sanket Patil An Overview of Complex Networks Design and Analyses
  98. 98. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Robustness Centrality Measures Connectivity Sanket Patil An Overview of Complex Networks Design and Analyses
  99. 99. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Robustness Centrality Measures Connectivity Sanket Patil An Overview of Complex Networks Design and Analyses
  100. 100. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Centrality Degree Centrality: degree distribution Betweenness: importance of nodes based on the no. of paths passing through them Closeness: per node average path length Eigenvector Centrality: importance of nodes based not just on how many are endorsing, but also who is connected. When a centrality distribution is uniform, the network is most robust Sanket Patil An Overview of Complex Networks Design and Analyses
  101. 101. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Centrality Degree Centrality: degree distribution Betweenness: importance of nodes based on the no. of paths passing through them Closeness: per node average path length Eigenvector Centrality: importance of nodes based not just on how many are endorsing, but also who is connected. When a centrality distribution is uniform, the network is most robust Sanket Patil An Overview of Complex Networks Design and Analyses
  102. 102. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Centrality Degree Centrality: degree distribution Betweenness: importance of nodes based on the no. of paths passing through them Closeness: per node average path length Eigenvector Centrality: importance of nodes based not just on how many are endorsing, but also who is connected. When a centrality distribution is uniform, the network is most robust Sanket Patil An Overview of Complex Networks Design and Analyses
  103. 103. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Centrality Degree Centrality: degree distribution Betweenness: importance of nodes based on the no. of paths passing through them Closeness: per node average path length Eigenvector Centrality: importance of nodes based not just on how many are endorsing, but also who is connected. When a centrality distribution is uniform, the network is most robust Sanket Patil An Overview of Complex Networks Design and Analyses
  104. 104. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Centrality Degree Centrality: degree distribution Betweenness: importance of nodes based on the no. of paths passing through them Closeness: per node average path length Eigenvector Centrality: importance of nodes based not just on how many are endorsing, but also who is connected. When a centrality distribution is uniform, the network is most robust Sanket Patil An Overview of Complex Networks Design and Analyses
  105. 105. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Connectivity Connected, strongly connected and weakly connected Vertex Cut: The smallest number of vertices whose removal renders the network disconnected Edge Cut: The smallest number od edges whose removal renders the network disconnected A graph is k − connected if the size of its vertex cut is k Higher the connectivity, more robust the network Sanket Patil An Overview of Complex Networks Design and Analyses
  106. 106. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Connectivity Connected, strongly connected and weakly connected Vertex Cut: The smallest number of vertices whose removal renders the network disconnected Edge Cut: The smallest number od edges whose removal renders the network disconnected A graph is k − connected if the size of its vertex cut is k Higher the connectivity, more robust the network Sanket Patil An Overview of Complex Networks Design and Analyses
  107. 107. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Connectivity Connected, strongly connected and weakly connected Vertex Cut: The smallest number of vertices whose removal renders the network disconnected Edge Cut: The smallest number od edges whose removal renders the network disconnected A graph is k − connected if the size of its vertex cut is k Higher the connectivity, more robust the network Sanket Patil An Overview of Complex Networks Design and Analyses
  108. 108. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Connectivity Connected, strongly connected and weakly connected Vertex Cut: The smallest number of vertices whose removal renders the network disconnected Edge Cut: The smallest number od edges whose removal renders the network disconnected A graph is k − connected if the size of its vertex cut is k Higher the connectivity, more robust the network Sanket Patil An Overview of Complex Networks Design and Analyses
  109. 109. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Connectivity Connected, strongly connected and weakly connected Vertex Cut: The smallest number of vertices whose removal renders the network disconnected Edge Cut: The smallest number od edges whose removal renders the network disconnected A graph is k − connected if the size of its vertex cut is k Higher the connectivity, more robust the network Sanket Patil An Overview of Complex Networks Design and Analyses
  110. 110. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Independent/Disjoint Paths Two paths are vertex independent if they have no common vertices (except the terminals) Two paths are edge independent if they have no common edges Menger’s Theorem: Max-flow min-cut More independent paths implies higher robustness Sanket Patil An Overview of Complex Networks Design and Analyses
  111. 111. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Independent/Disjoint Paths Two paths are vertex independent if they have no common vertices (except the terminals) Two paths are edge independent if they have no common edges Menger’s Theorem: Max-flow min-cut More independent paths implies higher robustness Sanket Patil An Overview of Complex Networks Design and Analyses
  112. 112. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Independent/Disjoint Paths Two paths are vertex independent if they have no common vertices (except the terminals) Two paths are edge independent if they have no common edges Menger’s Theorem: Max-flow min-cut More independent paths implies higher robustness Sanket Patil An Overview of Complex Networks Design and Analyses
  113. 113. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Independent/Disjoint Paths Two paths are vertex independent if they have no common vertices (except the terminals) Two paths are edge independent if they have no common edges Menger’s Theorem: Max-flow min-cut More independent paths implies higher robustness Sanket Patil An Overview of Complex Networks Design and Analyses
  114. 114. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Number of connected components Robustness can be measured in terms of the number of components that result due to failures Size of the connected components also matters in many cases Toughness: A toughness of t means, for a given number k(> 1), at least t ∗ k nodes need to be removed to fragment the graph into k connected components Graph Toughness: Biggest value of t Sanket Patil An Overview of Complex Networks Design and Analyses
  115. 115. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Number of connected components Robustness can be measured in terms of the number of components that result due to failures Size of the connected components also matters in many cases Toughness: A toughness of t means, for a given number k(> 1), at least t ∗ k nodes need to be removed to fragment the graph into k connected components Graph Toughness: Biggest value of t Sanket Patil An Overview of Complex Networks Design and Analyses
  116. 116. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Number of connected components Robustness can be measured in terms of the number of components that result due to failures Size of the connected components also matters in many cases Toughness: A toughness of t means, for a given number k(> 1), at least t ∗ k nodes need to be removed to fragment the graph into k connected components Graph Toughness: Biggest value of t Sanket Patil An Overview of Complex Networks Design and Analyses
  117. 117. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Number of connected components Robustness can be measured in terms of the number of components that result due to failures Size of the connected components also matters in many cases Toughness: A toughness of t means, for a given number k(> 1), at least t ∗ k nodes need to be removed to fragment the graph into k connected components Graph Toughness: Biggest value of t Sanket Patil An Overview of Complex Networks Design and Analyses
  118. 118. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Conclusions Complex Networks design have non-trivial topological properties Structure governs function Designed for efficiency under constraints of robustness and cost Graph thoretic measures are useful for design and analyses Sanket Patil An Overview of Complex Networks Design and Analyses
  119. 119. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Conclusions Complex Networks design have non-trivial topological properties Structure governs function Designed for efficiency under constraints of robustness and cost Graph thoretic measures are useful for design and analyses Sanket Patil An Overview of Complex Networks Design and Analyses
  120. 120. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Conclusions Complex Networks design have non-trivial topological properties Structure governs function Designed for efficiency under constraints of robustness and cost Graph thoretic measures are useful for design and analyses Sanket Patil An Overview of Complex Networks Design and Analyses
  121. 121. Outline Introduction Topological Features Philosophy Design Analyses Conclusions Conclusions Complex Networks design have non-trivial topological properties Structure governs function Designed for efficiency under constraints of robustness and cost Graph thoretic measures are useful for design and analyses Sanket Patil An Overview of Complex Networks Design and Analyses
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