The past few decades have seen the rise of online social networks as a worldwide phenomenon with a high impact on our society. Beyond the obvious exposure phenomena, with obvious implications on security and privacy, people have started to become acquainted - even married! - in online social networks. In parallel, we have seen an enormous growth in terms of the number of published articles in computer science, mathematics and physics that study the organization of such networks. The availability of large free databases of friendships, collaborations and citations have made possible to study social networks at a scale and with a precision previously unknown.This issue of Internet Mathematics, titled “Searching and Mining the Web and Social Networks" was born out of the interest of the editors in the problem of searching and analyzing not only the web, but also social networks in a broad sense. In particular, we aimed to publish a collection of articles that take a rigorous mathematical viewpoint on problems most important and common in network applications. The general topics represented in this special issue cover ranking of the nodes, network measurements, and adversarial behavior. Each of these topics has received a large attention in the literature. We believe however that the originality of the articles presented in this volume is in a high level of mathematical rigor.