Advances in Network Complexity (Quantitative and Network Biology Series)

Hardcover, xiv+293pp, NOT ex-library. Clean and bright throughout, unmarked text, no inscriptions, no stamps, firmly bound. A minor crease to the lower outer corner of last pages. Short creases to board corners. Issued without a dust jacket. -- A well-balanced overview of mathematical approaches to complex systems ranging from applications in chemistry and ecology to basic research questions on network complexity. Well-known pioneers in the field have edited this volume with a view to balancing classical and modern approaches to ensure broad coverage of contemporary research problems. It is a valuable addition to the literature and a must-have for anyone dealing with network complexity and complexity issues. -- Contents: 1 Functional Complexity Based on Topology [Measure for the Functional Complexity of Networks; Applications] 2 Connections Between Artificial Intelligence & Computational Complexity & Complexity of Graphs [Representation & Searching Methods; Turing Machines; Fuzzy Logic & Graphs; Fuzzy Optimization & Systems; Problems Related to AI; Topology of Complex Networks; Hierarchies; Graph Entropy; Kolmogorov Complexity] 3 Selection-Based Estimates of Complexity Unravel Some Mechanisms & Selective Pressures Underlying the Evolution of Complexity in Artificial Networks [Complexity & Evolution; Macroscopic Quantification of Organismal Complexity; Selection-Based Methods of Complexity; Informational Complexity; Fisher Geometric Model; Cost of Complexity; Quantifying Phenotypic Complexity; Darwinian Adaptive Neural Networks DANN; Different Facets of Complexity; Mechanistic Understanding of Phenotypic Complexity; Selective Pressures Acting on Phenotypic Complexity] 4 Three Types of Network Complexity Pyramid [First Type: Life's Complexity Pyramid LCP; Second Type: Network Model Complexity Pyramid; Third Type: Generalized Farey Organized Network Pyramid] 5 Computational Complexity of Graphs [Star Complexity of Graphs; From Graphs to Boolean Functions; Formula Complexity of Graphs; Lower Bounds via Graph Entropy; Depth-2 & Depth-3 Complexity; Network Complexity of Graphs] 6 Linear Complexity of a Graph [Rationale & Approach; Background; Exploration of Irreducible Graphs; Bounds on the Linear Complexity of Graphs; Some Families of Graphs; Bounds for Graphs in General] 7 Kirchhoff's Matrix-Tree Theorem Revisited: Counting Spanning Trees with the Quantum Relative Entropy [Main Result; Bounds] 8 Dimension Measure for Complex Networks [Volume Dimension; Complex Network Zeta Function & Relation to Kolmogorov Complexity; Comparison with Complexity Classes; Node-Based Definition; Linguistic-Analysis Application; Statistical Mechanics Application; Function Values; Other Work on Complexity Measures] 9 Information-Based Complexity of Networks [History & Concept of Information-Based Complexity; Mutual Information; Graph Theory & Graph Theoretic Measures: Cyclomatic Number, Spanning Trees; Erdos-Renyi Random Graphs, Small World Networks, Scale-free Networks; Graph Entropy; Information-Based Complexity of Unweighted, Unlabeled & Undirected Networks; Motif Expansion; Labeled Networks; Weighted Networks; Empirical Results of Real Network Data & Artificially Generated Networks; Extension to Processes on Networks; Transfer Entropy; Medium Articulation] 10 Thermodynamic Depth in Undirected & Directed Networks [Polytopal vs Heat Flow Complexity; Characterization of Polytopal & Flow Complexity; Laplacian of a Directed Graph; Directed Heat Kernels & Heat Flow; Heat Flow-Thermodynamic Depth Complexity; Experimental Results] 11 Circumscribed Complexity in Ecological Networks [New Metaphor; Entropy as a Descriptor of Structure; Addressing Both Topology & Magnitude; Amalgamating Topology with Magnitudes; Effective Network Attributes; Limits to Complexity; Example Ecosystem Network; New Window on Complex Dynamics] 12 Metros as Biological Systems: Complexity in Small Real-life Networks [Methodology; Interpreting Complexity; Network Centrality]; Index.…