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Network Science
by Carlos Andre Reis Pinheiro
Network Science
Cover
Title Page
Copyright Page
Dedication Page
Preface
Acknowledgments
About the Author
About the Book
1 Concepts in Network Science
2 Subnetwork Analysis
3 Network Centralities
4 Network Optimization
5 Real‐World Applications in Network Science
Index
End User License Agreement
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Prev
Previous Chapter
Cover
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Next Chapter
Title Page
Table of Contents
Cover
Title Page
Copyright Page
Dedication Page
Preface
Acknowledgments
About the Author
About the Book
1 Concepts in Network Science
1.1 Introduction
1.2 The Connector
1.3 History
1.4 Concepts
1.5 Network Analytics
1.6 Summary
2 Subnetwork Analysis
2.1 Introduction
2.2 Connected Components
2.3 Biconnected Components
2.4 Community
2.5 Core
2.6 Reach Network
2.7 Network Projection
2.8 Node Similarity
2.9 Pattern Matching
2.10 Summary
3 Network Centralities
3.1 Introduction
3.2 Network Metrics of Power and Influence
3.3 Degree Centrality
3.4 Influence Centrality
3.5 Clustering Coefficient
3.6 Closeness Centrality
3.7 Betweenness Centrality
3.8 Eigenvector Centrality
3.9 PageRank Centrality
3.10 Hub and Authority
3.11 Network Centralities Calculation by Group
3.12 Summary
4 Network Optimization
4.1 Introduction
4.2 Clique
4.3 Cycle
4.4 Linear Assignment
4.5 Minimum‐Cost Network Flow
4.6 Maximum Network Flow Problem
4.7 Minimum Cut
4.8 Minimum Spanning Tree
4.9 Path
4.10 Shortest Path
4.11 Transitive Closure
4.12 Traveling Salesman Problem
4.13 Vehicle Routing Problem
4.14 Topological Sort
4.15 Summary
5 Real‐World Applications in Network Science
5.1 Introduction
5.2 An Optimal Tour Considering a Multimodal Transportation System – The Traveling Salesman Problem Example in Paris
5.3 An Optimal Beer Kegs Distribution – The Vehicle Routing Problem Example in Asheville
5.4 Network Analysis and Supervised Machine Learning Models to Predict COVID‐19 Outbreaks
5.5 Urban Mobility in Metropolitan Cities
5.6 Fraud Detection in Auto Insurance Based on Network Analysis
5.7 Customer Influence to Reduce Churn and Increase Product Adoption
5.8 Community Detection to Identify Fraud Events in Telecommunications
5.9 Summary
Index
End User License Agreement
List of Illustrations
Chapter 1
Figure 1.1 Directed and undirected links with weighted nodes.
Figure 1.2 Representation of a directed graph with weighted nodes and links....
Figure 1.3 A matrix representation for a graph.
Figure 1.4 A table representation for a graph.
Figure 1.5 Representation of the three types of graphs, regular, small world...
Figure 1.6 Random graph.
Figure 1.7 Regular graph.
Figure 1.8 Graph representing four legislators working in committees.
Figure 1.9 Four graphs with same number of nodes and different number of lin...
Figure 1.10 Four graphs with same number of nodes but different number of li...
Figure 1.11 Largest component, diameter, and average path for the four graph...
Figure 1.12 Ratio of the size of components and the diameter.
Figure 1.13 Les Misérables network.
Figure 1.14 Summary statistics results.
Figure 1.15 Summary statistics for the Les Misérables network.
Figure 1.16 Output data for the nodes.
Figure 1.17 Output data for the links.
Chapter 2
Figure 2.1 (a) Graph (b) Subgraph (c) Induced graph.
Figure 2.2 (a) Graph (b) Links selection (c) Subgraph by links selection.
Figure 2.3 (a) Graph (b) Subgraph by removing nodes.
Figure 2.4 (a) Graph (b) Subgraphs by removing links.
Figure 2.5 Subgraph
G
′
isomorphic to graph
H
.
Figure 2.6 Input graph with undirected links.
Figure 2.7 Output results by proc network running the connected components a...
Figure 2.8 Output nodes table for the connected components.
Figure 2.9 Output links table for the connected components.
Figure 2.10 Output summary table for the connected components.
Figure 2.11 Input graph with undirected links.
Figure 2.12 Output results by proc network running connected components on u...
Figure 2.13 Output links table for the connected components.
Figure 2.14 Output nodes table for the connected components.
Figure 2.15 Output summary table for the connected components.
Figure 2.16 Input graph with undirected links and the identified connected c...
Figure 2.17 Input graph with directed links.
Figure 2.18 Output results by proc network running connected components on a...
Figure 2.19 Output links table for the connected components.
Figure 2.20 Output nodes table for the connected components.
Figure 2.21 Output summary table for the connected components.
Figure 2.22 Input graph with directed links and the identified connected com...
Figure 2.23 Input graph with undirected links for the biconnected components...
Figure 2.24 Output results by proc network for the biconnected components al...
Figure 2.25 Output links table for the biconnected components.
Figure 2.26 Output nodes table for the biconnected components.
Figure 2.27 Output summary table for the biconnected components.
Figure 2.28 Input graph with the identified biconnected components and the a...
Figure 2.29 Aggregating directed links into undirected links.
Figure 2.30 Input graph with undirected weighted links.
Figure 2.31 Output summary results for the community detection on an undirec...
Figure 2.32 Output communities level table for the community detection.
Figure 2.33 Output nodes table for the community detection.
Figure 2.34 Output links table for the community detection.
Figure 2.35 Output overlap table for the community detection.
Figure 2.36 Output communities' attributes table for the community detection...
Figure 2.37 Output communities' links table for the community detection.
Figure 2.38 Communities identified by the Louvain algorithm.
Figure 2.39 Output communities' level table for the community detection.
Figure 2.40 Output nodes table for the community detection.
Figure 2.41 Communities identified by the label propagation algorithm.
Figure 2.42 Output communities' level table for the community detection.
Figure 2.43 Output nodes table for the community detection.
Figure 2.44 Communities identified by the label propagation algorithm with t...
Figure 2.45 Input graph with directed weighted links.
Figure 2.46 Output communities' level table for the community detection.
Figure 2.47 Output nodes table for the community detection.
Figure 2.48 Communities identified by the parallel label propagation algorit...
Figure 2.49 Output communities' level table for the community detection.
Figure 2.50 Output nodes table for the community detection.
Figure 2.51 Communities identified by the label propagation algorithm with t...
Figure 2.52 Output communities' level table for the community detection.
Figure 2.53 Output nodes table for the community detection.
Figure 2.54 Communities identified by the label propagation algorithm with t...
Figure 2.55 Input graph with undirected links.
Figure 2.56 Output summary results for the k‐core decomposition on an undire...
Figure 2.57 Output for the k‐cores and the assigned nodes.
Figure 2.58 The undirected input graph highlighting the cores and the nodes ...
Figure 2.59 Cores identified by the k‐core decomposition algorithm.
Figure 2.60 Cores out identified by the k‐core decomposition algorithm.
Figure 2.61 Cores out highlighted in the directed network.
Figure 2.62 Cores in highlighted in the directed network.
Figure 2.63 Input graph with undirected and unweighted links.
Figure 2.64 Output results by proc network running the reach network algorit...
Figure 2.65 Output nodes table for the reach network.
Figure 2.66 Output links table for the reach network.
Figure 2.67 Output links table for the reach network.
Figure 2.68 Input graph with the reach networks highlighted.
Figure 2.69 Counts table for the node A using maximum reach equals 2.
Figure 2.70 Counts for all reach networks considering all nodes as source.
Figure 2.71 Directed links for node D.
Figure 2.72 Counts for the reach network assigned to node D.
Figure 2.73 Input bipartite graph.
Figure 2.74 Output results by proc network running the network projection al...
Figure 2.75 Output nodes for the projected network.
Figure 2.76 Output links for the projected network.
Figure 2.77 Output common neighbors for the projected network.
Figure 2.78 Projected network.
Figure 2.79 Input bipartite graph.
Figure 2.80 Output nodes for the projected network.
Figure 2.81 Output links for the projected network.
Figure 2.82 Output common neighbors for the projected network.
Figure 2.83 Projected network.
Figure 2.84 Similar nodes based on their neighborhood.
Figure 2.85 Similar nodes based on their structural role proximity.
Figure 2.86 Input undirected graph.
Figure 2.87 Output results by proc network running the node similarity algor...
Figure 2.88 Output vectors for the node similarity.
Figure 2.89 Output node similarity measures.
Figure 2.90 Output node similarity for the top Jaccard measure.
Figure 2.91 Output node similarity measures for the pair of nodes A and T.
Figure 2.92 Output nodes similarity.
Figure 2.93 Node similarity outcomes.
Figure 2.94 Output node similarity measures for a directed graph.
Figure 2.95 Four patterns in a path of sequential transactions.
Figure 2.96 The main graph with undirected links.
Figure 2.97 The query graph.
Figure 2.98 Output results by proc network running the pattern matching algo...
Figure 2.99 Output nodes table for the pattern matching algorithm.
Figure 2.100 Output links table for the pattern matching algorithm.
Figure 2.101 Pattern matching outcome.
Figure 2.102 The main graph with directed links.
Figure 2.103 The query graph with directed links.
Figure 2.104 Output nodes table for the pattern matching algorithm for a dir...
Figure 2.105 Output links table for the pattern matching algorithm for a dir...
Figure 2.106 Pattern matching outcome on the directed graph.
Chapter 3
Figure 3.1 Network graph containing nodes and links.
Figure 3.2 Undirected graph representing the connections of node A.
Figure 3.3 Directed graph representing the connections of node A, considerin...
Figure 3.4 Output results by proc network.
Figure 3.5 Output dataset for the nodes based on an undirected graph with un...
Figure 3.6 Output dataset for the links.
Figure 3.7 Output dataset for the nodes based on a directed graph with unwei...
Figure 3.8 Directed graph with weighted links.
Figure 3.9 Output dataset for the nodes considering weighted and unweighted ...
Figure 3.10 Output dataset for the nodes based on an undirected graph with w...
Figure 3.11 Output dataset for the links based on an undirected graph with w...
Figure 3.12 Network analysis object in visual analytics with the original li...
Figure 3.13 Network analysis objects in visual analytics with links dataset ...
Figure 3.14 HTM file containing the graph to be plotted.
Figure 3.15 Download the visnet.htm file.
Figure 3.16 Open the visnet.htm file in a browser.
Figure 3.17 The graph plotted by the visnet.htm file containing the links da...
Figure 3.18 Les Miserables dataset plotted in vis.js.
Figure 3.19 Undirected graph with link weights to compute influence centrali...
Figure 3.20 Output nodes dataset containing the influence centrality results...
Figure 3.21 Output nodes dataset containing the influence centrality results...
Figure 3.22 Directed graph to compute influence centrality.
Figure 3.23 Output nodes dataset containing the influence centrality results...
Figure 3.24 Output nodes dataset containing the influence centrality results...
Figure 3.25 Undirected graph to compute the clustering coefficient centralit...
Figure 3.26 Output nodes dataset containing the clustering coefficient centr...
Figure 3.27 Directed graph to compute the clustering coefficient centrality....
Figure 3.28 Output nodes dataset containing the clustering coefficient centr...
Figure 3.29 Undirected graph to compute closeness.
Figure 3.30 Undirected graph with inversed weights.
Figure 3.31 Output nodes dataset containing the closeness centrality results...
Figure 3.32 Output nodes dataset containing the closeness centrality results...
Figure 3.33 Directed graph with original weights.
Figure 3.34 Directed graph with inversed weights.
Figure 3.35 Output nodes dataset containing the closeness centrality results...
Figure 3.36 Output nodes dataset containing the closeness centrality results...
Figure 3.37 Undirected graph with original weights.
Figure 3.38 Undirected graph with inversed weights to compute the betweennes...
Figure 3.39 Output nodes dataset containing the betweenness centrality resul...
Figure 3.40 Output links dataset containing the link betweenness centrality ...
Figure 3.41 Output nodes dataset containing the betweenness centrality resul...
Figure 3.42 Directed graph with original weights.
Figure 3.43 Directed graph with inversed weights to compute the betweenness ...
Figure 3.44 Output nodes dataset containing the betweenness centrality resul...
Figure 3.45 Output nodes dataset containing the betweenness centrality resul...
Figure 3.46 Output links dataset containing the link betweenness centrality ...
Figure 3.47 Output nodes dataset containing the betweenness centrality resul...
Figure 3.48 Output nodes dataset containing the betweenness centrality resul...
Figure 3.49 Undirected graph to shows eigenvector centrality.
Figure 3.50 Output nodes dataset containing the eigenvector centrality based...
Figure 3.51 Output nodes dataset containing the eigenvector centrality based...
Figure 3.52 Directed graph to shows eigenvector centrality.
Figure 3.53 Output nodes dataset containing the eigenvector centrality based...
Figure 3.54 Output nodes dataset containing the eigenvector centrality based...
Figure 3.55 Directed graph with unweighted links to shows PageRank centralit...
Figure 3.56 Directed graph with link weights evenly distributed.
Figure 3.57 Output nodes dataset containing the PageRank centrality based on...
Figure 3.58 Undirected graph with weighted links to show the PageRank centra...
Figure 3.59 Output nodes dataset containing the PageRank centrality based on...
Figure 3.60 Undirected graph with unweighted links to show the PageRank cent...
Figure 3.61 Output nodes dataset containing the PageRank centrality based on...
Figure 3.62 Directed graph to shows the PageRank centrality calculation.
Figure 3.63 Output nodes dataset containing the PageRank centrality based on...
Figure 3.64 Directed graph to shows hub and authority centralities.
Figure 3.65 Output nodes dataset containing the hub and authority centraliti...
Figure 3.66 Output nodes dataset containing the hub and authority centraliti...
Figure 3.67 Directed graph with weighted links to demonstrate the hub and au...
Figure 3.68 Output nodes dataset containing the hub and authority centraliti...
Figure 3.69 Output nodes dataset containing all the network centralities res...
Figure 3.70 Output links dataset containing the link betweenness centrality ...
Figure 3.71 Directed graph used to compute the network centralities.
Figure 3.72 Output nodes dataset containing the community identification for...
Figure 3.73 Directed graph comprising two communities.
Figure 3.74 Output nodes dataset containing the community identification for...
Figure 3.75 Output nodes dataset containing the network centralities by grou...
Figure 3.76 Output nodes dataset containing the original degree centrality f...
Chapter 4
Figure 4.1 Map by Merian‐Erben (1652) showing the city of Königsberg.
Figure 4.2 Euler's drawing of the Königsberg bridges.
Figure 4.3 Königsberg bridges as links and distinct mainlands as nodes.
Figure 4.4 Königsberg bridges problem as nodes and links.
Figure 4.5 Undirected graph with weighted links.
Figure 4.6 Summary results for clique enumeration using proc optnetwork.
Figure 4.7 Output dataset for the cliques.
Figure 4.8 Output results for proc optnetwork searching for cliques.
Figure 4.9 Output dataset with the nodes within the single clique.
Figure 4.10 Single clique within the network based on a set of constraints....
Figure 4.11 No cliques found with a minimum of 5 nodes.
Figure 4.12 Directed graph with unweighted links.
Figure 4.13 Summary results for cycle enumeration using proc optnetwork.
Figure 4.14 Output dataset containing the nodes within the cycle.
Figure 4.15 Output dataset containing the cycles.
Figure 4.16 Single cycle within the input graph.
Figure 4.17 Bipartite graph with relations between workers and tasks.
Figure 4.18 Matrix workers by pieces of a chair containing the respective co...
Figure 4.19 Table of workers containing the costs to produce each piece of a...
Figure 4.20 Output results by proc optnetwork.
Figure 4.21 Table of selected workers and the costs to produce each piece of...
Figure 4.22 Bipartite graph with the optimal match.
Figure 4.23 Table containing the inverse of the weights.
Figure 4.24 Output results produced by proc optnetwork.
Figure 4.25 Table of selected workers and the costs to produce each piece of...
Figure 4.26 Network flow with costs and lower and upper bounds for nodes and...
Figure 4.27 Output results by proc optnetwork running the minimum‐cost netwo...
Figure 4.28 The minimum‐cost network flow solution for the links.
Figure 4.29 The minimum‐cost network flow solution for the nodes.
Figure 4.30 Minimum‐cost network flow results.
Figure 4.31 Output by proc optnetwork running the minimum‐cost network flow ...
Figure 4.32 The minimum‐cost network flow solution for the links.
Figure 4.33 Minimum‐cost network flow results for the flexible network.
Figure 4.34 Output by proc optnetwork showing that there is no feasible solu...
Figure 4.35 Output by proc optnetwork showing a feasible solution for the ne...
Figure 4.36 Network flow with upper limits of flow in each link.
Figure 4.37 Output results by proc optnetwork running the maximum network fl...
Figure 4.38 The maximum network flow solution for the links.
Figure 4.39 Maximum network flow results.
Figure 4.40 Output results by proc optnetwork running the maximum network fl...
Figure 4.41 Maximum network flow results.
Figure 4.42 Maximum network flow results.
Figure 4.43 Image in pixels represented by nodes and links.
Figure 4.44 Undirected graph with weighted links.
Figure 4.45 Output results by proc optnetwork running the minimum cut algori...
Figure 4.46 Result table for the partitions in the minimum cut problem.
Figure 4.47 Results table for the cut sets in the minimum cut problem.
Figure 4.48 Minimum cut sets for the input graph.
Figure 4.49 Directed graph with weighted links.
Figure 4.50 Result table for the partitions in the minimum s‐t cut problem....
Figure 4.51 Results table for the cut sets in the minimum s‐t cut problem.
Figure 4.52 Minimum s‐t cut problem.
Figure 4.53 Network flow nodes and weighted links.
Figure 4.54 Output results by proc optnetwork running the minimum spanning t...
Figure 4.55 The minimum spanning tree solution.
Figure 4.56 Minimum spanning tree results.
Figure 4.57 Directed input graph with weighted links.
Figure 4.58 Output results by proc optnetwork running the path enumeration a...
Figure 4.59 The path enumeration solution for the links.
Figure 4.60 The path enumeration solution for the nodes.
Figure 4.61 The path enumeration solution with a fixed source node.
Figure 4.62 The path enumeration solution for the links using a fixed source...
Figure 4.63 The path enumeration solution with a fixed sink node.
Figure 4.64 The path enumeration solution for the links using a fixed sink n...
Figure 4.65 The path enumeration solution for fixed source and sink nodes.
Figure 4.66 The path enumeration solution for the links using fixed source a...
Figure 4.67 Input graph with fixed source and sink nodes.
Figure 4.68 The path enumeration solution for the nodes.
Figure 4.69 Output results by proc optnetwork running the path enumeration a...
Figure 4.70 The path enumeration solution for the links.
Figure 4.71 The path enumeration solution for the nodes.
Figure 4.72 Directed input graph with weighted links.
Figure 4.73 Output results by proc optnetwork running the shortest path algo...
Figure 4.74 The shortest path solution for the links.
Figure 4.75 The shortest path solution for the nodes.
Figure 4.76 The sum of link weights of the shortest paths.
Figure 4.77 The sum of link weights of the shortest paths A‐B, A‐C, and C‐D....
Figure 4.78 The summary statistics for the shortest path solution.
Figure 4.79 The shortest path solution with a fixed source node.
Figure 4.80 The shortest path solution for the links using a fixed source no...
Figure 4.81 The shortest path solution with a fixed sink node.
Figure 4.82 The shortest path solution for the links using a fixed sink node...
Figure 4.83 The shortest path solution for fixed source and sink nodes.
Figure 4.84 The shortest path solution for the links using fixed source and ...
Figure 4.85 Input graph with fixed source and sink nodes.
Figure 4.86 Output results by proc optnetwork running the shortest path algo...
Figure 4.87 The number of links comprised in the shortest paths when proc op...
Figure 4.88 Links comprised in the shortest paths for the directed graph.
Figure 4.89 Links comprised in the shortest paths for the undirected graph....
Figure 4.90 Undirected graph based on the French movie Les Misérables.
Figure 4.91 Links comprised in the shortest paths for Les Misérables's undir...
Figure 4.92 Links comprised in the shortest paths for Les Misérables's direc...
Figure 4.93 Transitive closure from a directed input graph.
Figure 4.94 Directed input graph with unweighted links.
Figure 4.95 Output results by proc optnetwork running the transitive closure...
Figure 4.96 The transitive closure output.
Figure 4.97 The binary relation B‐E through three directed links within the ...
Figure 4.98 Output results by proc optnetwork running the transitive closure...
Figure 4.99 The transitive closure output for an undirected graph.
Figure 4.100 The undirected graph with bidirectional links between the nodes...
Figure 4.101 The transitive closure for the Les Misérables's network.
Figure 4.102 Undirected input graph with weighted links.
Figure 4.103 Output results by proc optnetwork running the traveling salesma...
Figure 4.104 The sequence of nodes in the traveling salesman problem output ...
Figure 4.105 The sequence of links in the traveling salesman problem output ...
Figure 4.106 The optimal tour generated by proc optnetwork based on an undir...
Figure 4.107 Directed input graph with weighted links.
Figure 4.108 Output results by proc optnetwork running the traveling salesma...
Figure 4.109 The sequence of nodes in the traveling salesman problem output ...
Figure 4.110 The sequence of links in the traveling salesman problem output ...
Figure 4.111 The optimal tour generated by proc optnetwork based on a direct...
Figure 4.112 Output results by proc optnetwork running the traveling salesma...
Figure 4.113 Directed input graph with the link (
A
,
H
,
3
).
Figure 4.114 Output results by proc optnetwork running the traveling salesma...
Figure 4.115 Undirected input graph with weighted links and nodes demands.
Figure 4.116 Output results by proc optnetwork running the vehicle routing p...
Figure 4.117 The set of store nodes and in which route and order they will b...
Figure 4.118 The order of the links for each route in the vehicle routing pr...
Figure 4.119 The vehicle routing problem solution generated by proc optnetwo...
Figure 4.120 The infeasible solution for the vehicle routing problem when us...
Figure 4.121 The feasible solution for the vehicle routing problem when usin...
Figure 4.122 The set of nodes and the demands.
Figure 4.123 The routes and the sequence of nodes.
Figure 4.124 The vehicle routing problem solution with a high vehicle maximu...
Figure 4.125 The vehicle routing problem based on a directed graph.
Figure 4.126 The solution for the vehicle routing problem with a high vehicl...
Figure 4.127 The vehicle routing problem based on a directed graph with addi...
Figure 4.128 The feasible solution for the vehicle routing problem based on ...
Figure 4.129 The set of nodes, the routes, and the sequence of nodes within ...
Figure 4.130 The routes and the sequence of nodes.
Figure 4.131 The vehicle routing problem solution based on a directed graph....
Figure 4.132 The first steps of the brewing process (USA Hops).
Figure 4.133 The directed graph representing task and their ordering.
Figure 4.134 Input graph with directed links.
Figure 4.135 Output results by proc optnetwork running the topological sort ...
Figure 4.136 The topological sort solution.
Figure 4.137 Solution for the topological sort.
Chapter 5
Figure 5.1 Places to be visited in the optimal tour in Paris.
Figure 5.2 Links considered in the network when searching for the optimal to...
Figure 5.3 Links considered in the network when searching for the optimal to...
Figure 5.4 Transportation network.
Figure 5.5 Cliques within the transportation network.
Figure 5.6 Cycles within the transportation network.
Figure 5.7 Minimum spanning tree within the transportation network.
Figure 5.8 Paths within the transportation network between two locations.
Figure 5.9 The shortest path between two locations within the transportation...
Figure 5.10 The Pattern Match within the transportation network.
Figure 5.11 The closest stations to the locations to be visited.
Figure 5.12 The final optimal tour considering the transportation network.
Figure 5.13 The brewery and the customers with their demands of beer kegs.
Figure 5.14 Customers located in downtown.
Figure 5.15 Output results from the VRP algorithm in proc optnetwork.
Figure 5.16 Output table with each route and its sequence.
Figure 5.17 Six routes for one truck with 23 capacity.
Figure 5.18 Route 1 considering one truck with 23 capacity.
Figure 5.19 Route 2 considering one truck with 23 capacity.
Figure 5.20 Route 3 considering one truck with 23 capacity.
Figure 5.21 Route 4 considering one truck with 23 capacity.
Figure 5.22 Route 5 considering one truck with 23 capacity.
Figure 5.23 Route 6 considering one truck with 23 capacity.
Figure 5.24 Routes considering two truck with 23 capacity.
Figure 5.25 Routes considering four truck with 30 capacity.
Figure 5.26 Population movement and COVID‐19 outbreaks over the weeks.
Figure 5.27 Communities based on the population movements.
Figure 5.28 Key cities highlighted by the network metrics and the hot spots ...
Figure 5.29 Key locations based on the network centrality measures.
Figure 5.30 Final links associated to the optimal tour.
Figure 5.31 Supervised machine learning models performance.
Figure 5.32 Outcomes of supervised machine learning models predicting outbre...
Figure 5.33 Inferred network of cases.
Figure 5.34 Frequent trajectories in the city of Rio de Janeiro.
Figure 5.35 Number of domiciles and workplaces by neighborhoods.
Figure 5.36 Geo map of the presumed domiciles and workplaces.
Figure 5.37 Frequent commuting paths in the city of Rio de Janeiro.
Figure 5.38 Traffic volume by day.
Figure 5.39 Distance traveled by subscribers.
Figure 5.40 Traffic and movements on weekdays and weekends.
Figure 5.41 Volume of movements in the city of Rio de Janeiro.
Figure 5.42 Possible alternative routes based on the overall population move...
Figure 5.43 Nodes and links assigned to an individual claim.
Figure 5.44 Relationships between claims due to same participants.
Figure 5.45 Network structure highlighting different types of participants....
Figure 5.46 Star network showing all connections of a doctor specialist.
Figure 5.47 Subnetworks considered as outliers.
Figure 5.48 Network analysis approach.
Figure 5.49 Profile of influencers and regular churners.
Figure 5.50 Likelihood of churn over time within the communities.
Figure 5.51 The viral effect of purchasing.
Figure 5.52 The overall process based on the social network analysis.
Figure 5.53 Rules and thresholds produced by the outlier analysis.
Figure 5.54 Outlier on the link weight and the hub centrality.
Figure 5.55 Outlier on the link weight, and hub and authority centralities....
Guide
Cover Page
Title Page
Copyright Page
Dedication Page
Preface
Acknowledgments
About the Author
About the Book
Table of Contents
Begin Reading
Index
Wiley End User License Agreement
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