In February 2024, the second Volume of the Random Graphs and Complex Networks book series has appeared. While Volume 1 is aimed at master students in mathematics and related fields, Volume 2 is aimed more towards the research community. This community includes PhD students and researchers, with a mathematical background. Having worked on it for some 17 years, it is quite a relief that it has finally appeared in press!
![](https://www.networkpages.nl/wp-content/uploads/2024/04/Picture2.jpg)
The book covers recent developments in random graphs theory about the local and global structure of random graphs. It is the first book covering the central notion of local convergence, a method that has had profound consequences in random graph theory. Many properties of random graphs can be understood by linking them to the random graph’s local limit.
![](https://www.networkpages.nl/wp-content/uploads/2024/04/Capture.png)
The relation between the chapters in Volumes 1 and 2.
Further, the book covers global properties, such as the existence of a giant connected component containing a positive proportion of the vertices in the graph, as well as when random graphs are fully connected. Another point of focus are the small-world properties of random graphs. The book closes with an extensive discussion on related random graphs models, discussing models that are directed, have a local or global community structure, or have a geometric structure. The book has some 300 exercises that allow readers to sharpen their familiarity with the topics that are discussed. It is online available on my personal website.
![](https://www.networkpages.nl/wp-content/uploads/2024/04/Picture1.jpg)