Alan Frieze is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University, Pennsylvania. He has authored more than 300 publications in top journals and was invited to be a plenary speaker at the Seoul ICM 2014. In 1991 he received the Fulkerson prize in discrete mathematics. Michał Karoński is a founder of the Discrete Mathematics Research group at Adam Mickiewicz University in Poznan, Poland. He has authored over 50 publications and currently serves as co-Editor-in-Chief of Random Structures and Algorithms.

• Preface; Part I. Basic Models: 1. Random graphs; 2. Evolution; 3. Vertex degrees; 4. Connectivity; 5. Small subgraphs; 6. Spanning subgraphs; 7. Extreme characteristics; 8. Extremal properties; Part II. Basic Model Extensions: 9. Inhomogeneous graphs; 10. Fixed degree sequence; 11. Intersection graphs; 12. Digraphs; 13. Hypergraphs; Part III. Other Models: 14. Trees; 15. Mappings; 16. k-out; 17. Real-world networks; 18. Weighted graphs; 19. Brief notes on uncovered topics; Part IV. Tools and Methods: 20. Moments; 21. Inequalities; 22. Differential equations method; 23. Branching processes; 24. Entropy; References; Author index; Main index.

'This is a well-planned book that is true to its title in that it is indeed accessible for anyone with just an undergraduate student's knowledge of enumerative combinatorics and probability.' Miklós Bóna, MAA Reviews