Synopsis
Uncover how deep randomness can go in graphs and why it matters
Discover how the depth of random graphs behaves as the size grows, with results that bound average depth and its distribution. This book presents rigorous proofs that link graph density to how far information must travel through the network.
The work focuses on depth in both undirected and directed random graphs, showing that under various edge probabilities the depth is typically proportional to a constant times log n. It offers a sequence of theorems and proofs that connect the graph’s structure to its depth, giving readers a precise sense of how quickly depth grows or shrinks as the graph expands.
- Clear statements about average depth and depth distribution for different p regimes
- Two-stage proof techniques and probabilistic reasoning, including BFS-style arguments
- Connections to classical results while highlighting new contributions for sparse and dense graphs
Ideal for readers of theoretical computer science, combinatorics, and network science who want rigorous, accessible insight into how random graph structures behave at scale.
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On the Depth of a Random Graph (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book investigates the depth of random graphs, a topic with important applications in computer science. The author introduces the concept of graph depth and provides a comprehensive analysis of the average and maximum depth of random graphs. The book presents new results on the depth of sparse and dense random graphs, providing valuable insights into the structure and connectivity of these graphs. The author also explores the relationship between the depth of a random graph and the probability of finding paths of a given length. By applying advanced mathematical techniques, the author provides a rigorous treatment of the subject, making this book an essential reference for researchers and practitioners working with random graphs. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332969036_0
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On the Depth of a Random Graph Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332969036
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On the Depth of a Random Graph Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332969036
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