  1. The birth of network science. 2. What are random networks? 3. Adjacency
matrix. 4. Degree distribution. 5. What are simple networks? Classical random
graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated
networks. 9. What are small worlds? 10. Real networks are mesoscopic objects.
11. What are complex networks? 12. The configuration model. 13. The absence of
degree--degree correlations. 14.Networks with correlated degrees.15.Clustering.
16. What are small-world networks? 17. `Small worlds' is not the same as
`small-world networks'. 18. Fat-tailed degree distributions. 19.Reasons for the
fat-tailed degree distributions. 20. Preferential linking. 21. Condensation of
edges. 22. Cut-offs of degree distributions. 23. Reasons for correlations in
networks. 24. Classical random graphs cannot be used for comparison with real
networks. 25. How to measure degree--degree correlations. 26. Assortative and
disassortative mixing. 27. Disassortative mixing does not mean that vertices of
high degrees rarely connect to each other. 28. Reciprocal links in directed
nets. 29. Ultra-small-world effect. 30. Tree ansatz. 31.Ultraresilience against
random failures. 32. When correlated nets are ultraresilient. 33. Vulnerability
of complex networks. 34. The absence of an epidemic threshold. 35. Search based
on local information. 36.Ultraresilience disappears in finite nets. 37.Critical
behavior of cooperative models on networks. 38. Berezinskii-Kosterlitz-Thouless
phase transitions in networks. 39.Cascading failures. 40.Cliques & communities.
41. Betweenness. 42.Extracting communities. 43. Optimal paths. 44.Distributions
of the shortest-path length & of the loop's length are narrow. 45. Diffusion on
networks. 46. What is modularity? 47.Hierarchical organization of networks. 48.
Convincing modelling of real-world networks:Is it possible? 49. The small Web..
