Complex Networks An Algorithmic Perspective

Network science is a rapidly emerging field of study that encompasses mathematics, computer science, physics, and engineering. A key issue in the study of complex networks is to understand the collective behavior of the various elements of these networks.Although the results from graph theory have proven to be powerful in investigating the structures of complex networks, few books focus on the algorithmic aspects of complex network analysis. Filling this need, Complex Networks: An Algorithmic Perspective supplies the basic theoretical algorithmic and graph theoretic knowledge needed by every researcher and student of complex networks.This book is about specifying, classifying, designing, and implementing mostly sequential and also parallel and distributed algorithms that can be used to analyze the static properties of complex networks. Providing a focused scope which consists of graph theory and algorithms for complex networks, the book identifies and describes a repertoire of algorithms that may be useful for any complex network. Provides the basic background in terms of graph theory Supplies a survey of the key algorithms for the analysis of complex networks Presents case studies of complex networks that illustrate the implementation of algorithms in real-world networks, including protein interaction networks, social networks, and computer networks Requiring only a basic discrete mathematics and algorithms background, the book supplies guidance that is accessible to beginning researchers and students with little background in complex networks. To help beginners in the field, most of the algorithms are provided in ready-to-be-executed form.While not a primary textbook, the author has included pedagogical features such as learning objectives, end-of-chapter summaries, and review questions

BACKGROUND IntroductionOverviewReal-World Complex Networks Technological Networks Information Networks Social Networks Biological Networks Topological Properties of Complex NetworksAlgorithmic ChallengesOutline of the BookReferencesGraph TheoryBasicsSubgraphsGraph IsomorphismTypes of GraphsPaths and CyclesConnectivityTreesGraph RepresentationsSpectral Properties of Graphs Eigenvalues and Eigenvectors The Laplacian MatrixChapter NotesReferencesAlgorithms and ComplexityIntroductionTime ComplexityRecurrencesDivide and Conquer AlgorithmsGraph Algorithms Breadth-first Search Depth-first SearchDynamic ProgrammingGreedy AlgorithmsNP-Complete Problems NP Completeness Reductions Satisfiability Problems 3-SAT to Independent Set Independent Set to Vertex Cover Independent Set to CliqueCoping with NP Completeness Backtracking Branch and BoundApproximation AlgorithmsParallel Algorithms Architectural Constraints Example AlgorithmsDistributed Systems and AlgorithmsChapter NotesReferencesAnalysis of Complex NetworksIntroductionVertex Degrees Degree Sequence Degree DistributionCommunities Clustering CoefficientThe Matching IndexCentralityNetwork MotifsModels Small World Networks Scale-Free NetworksChapter NotesReferencesALGORITHMS Distance and CentralityIntroductionFinding Distances Average Distance Dijkstra’s Single Source Shortest Paths Algorithm Floyd-Warshall All Pairs Shortest Paths AlgorithmCentrality Degree Centrality A Distributed Algorithm for k-hop Degree Centrality Closeness Centrality Stress CentralityBetweenness Centrality Newman’s Algorithm Brandes’ Algorithm Eigenvalue CentralityChapter NotesReferencesSpecial SubgraphsIntroductionMaximal Independent SetsDominating Sets A Greedy MDS Algorithm Guha-Khuller First MCDS Algorithm Guha-Khuller Second MCDS AlgorithmMatching A Maximal Unweighted Matching Algorithm A MaximalWeighted Matching AlgorithmVertex Cover A Minimal Connected Vertex Cover Algorithm A Minimal Weighted Vertex Cover AlgorithmA Distributed Algorithm for MWVC ConstructionChapter NotesReferencesData ClusteringIntroductionTypes of Data ClusteringAgglomerative Hierarchical Clusteringk-means AlgorithmNearest Neighbor AlgorithmFuzzy ClusteringDensity-based ClusteringParallel Data ClusteringChapter NotesReferencesGraph-based Clustering IntroductionGraph Partitioning BFS-based Partitioning Kernighan-Lin Algorithm Spectral Bisection Multi-level Partitioning Parallel PartitioningGraph Clustering MST-based Clustering Clustering with ClusterheadsDiscovery of Dense SubgraphsDefinitions Clique Algorithms The First Algorithm The Second Algorithm k-core AlgorithmChapter Notes References Network Motif Discovery IntroductionNetwork Motifs Measures of Motif Significance Generating Null Models Hardness of Motif DiscoverySubgraph Isomorphism Vertex Invariants Algorithms Ullman’s Algorithm Nauty Algorithm VF2 Algorithm BM1 AlgorithmMotif Discovery AlgorithmsExact Census Algorithms Mf inder Algorithm Enumerate Subgraphs (ESU) Algorithm Grochow and Kellis Algorithm Kavosh Algorithm MODA Approximate Algorithms with Sampling Mf inder with Sampling Randomized ESU Algorithm MODA with SamplingChapter NotesReferencesAPPLICATIONSProtein Interaction NetworksIntroductionTopological Properties of PPI NetworksDetection of Protein Complexes Highly Connected Subgraphs Algorithm Restricted Neighborhood Search Algorithm Molecular Complex Detection Algorithm Markov Clustering AlgorithmNetwork Motifs in PPI NetworksNetwork Alignment Quality of the Alignment Topological Similarity Node Similarity Algorithms PathBLAST MaWIsh IsoRank GRAAL Recent Algorithms Chapter Notes References Social NetworksIntroductionRelationships Homophily Positive and Negative Relations Structural BalanceEquivalenceCommunity Detection Algorithms Edge Betweenness-based Algorithm Resistor Networks RandomWalk Centrality Modularity-based Algorithm Chapter Notes References The Internet and the WebIntroductionThe Internet Services Services of Connection Circuit and Packet Switching Internet Protocol Suite Analysis The Web The Web Graph Properties Models Evolving Model Copying Model Growth-deletion Model Multi-layer Model Cyber Community Detection Link Analysis Hubs and Authorities Page Rank AlgorithmChapter Notes References Ad hoc Wireless NetworksIntroductionClustering Algorithms Lowest-ID Algorithm Dominating Set-based Clustering Spanning Tree-based ClusteringMobile Social Networks Architecture Community Detection Middleware MobiSoC MobiClique SAMOA YartaChapter NotesReferencesIndex

Kayhan Erciyes is a professor of computer science and engineering and also the rector of Izmir University, Izmir, Turkey. Dr. Erciyes worked as a research and development engineer of Alcatel Turkey, Alcatel Portugal, and Alcatel SEL. He has worked as faculty in Oregon State University, UC Davis and California State University, US and Izmir and Aegean universities. His research interests are on distributed systems, graph theory and distributed algorithms for complex networks, mobile ad hoc networks, wireless sensor networks and the Grid and has published extensively in these areas. Dr. Erciyes is the designer and implementer of one of the first commercially available MODEMs in Turkey