Each chapter contains numerous fully worked-out examples, plus a large set of practice problems with answers – ideal for exam preparation.
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Smarajit Ghosh is a renowned name in Electrical and Electronics Engineering, and his textbook "Network Theory: Analysis and Synthesis" is a staple for students preparing for university exams and competitive tests like GATE or ESE. Graphs and Basic Properties 2
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| | Chapter(s) | Core Topics | |----------|----------------|-----------------| | Part I – Foundations | 1. Graphs and Basic Properties 2. Paths, Cycles, Trees 3. Connectivity and Cuts | Formal definitions, adjacency/incidence matrices, Eulerian & Hamiltonian concepts | | Part II – Algebraic and Spectral Tools | 4. Matrix Representations of Graphs 5. Eigenvalues, Spectral Graph Theory 6. Laplacian Matrices | Spectral clustering, Cheeger inequality, graph partitioning | | Part III – Random Graphs | 7. Erdős–Rényi Model 8. Configuration Model 9. Preferential Attachment & Scale‑Free Networks | Phase transitions, degree distributions, clustering coefficients | | Part IV – Network Dynamics | 10. Diffusion Processes (random walks, PageRank) 11. Epidemic Spreading Models 12. Synchronization | Mean‑field approximations, threshold phenomena | | Part V – Algorithms and Applications | 13. Shortest‑Path & Flow Algorithms 14. Community Detection 15. Network Optimization (facility location, sensor placement) | Greedy, spectral, and modularity‑based methods | | Part VI – Advanced Topics | 16. Temporal and Multiplex Networks 17. Network Robustness & Resilience 18. Graph Neural Networks (introductory) | Edge dynamics, percolation, recent ML‑driven techniques | | Appendices | A. Proofs of Selected Theorems B. Mathematical Background C. Software Tools (NetworkX, igraph) | Supplemental material and code snippets | | References & Index | Comprehensive bibliography and subject index | |
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