A generalization of PageRank for the case of ranking two interacting groups of objects was described in [30] In applications it may be necessary to model systems having objects of two kinds where a weighted relation is defined on object pairs. This leads to considering bipartite graphs. For such graphs two related positive or nonnegative irreducible matrices corresponding to vertex partition sets can be defined. One can compute rankings of objects in both groups as eigenvectors corresponding to the maximal positive eigenvalues of these matrices. Normed eigenvectors exist and are unique by the Perron or Perron-Frobenius theorem. Example: consumers and products. the relation weight is the product consumption rate.
In February 1998 Jeffrey Brewer of Goto.com, a 25-employee startup company (later Overture, now part of Yahoo!), presented a pay per click search engine proof-of-concept to the TED conference in California.[11] This presentation and the events that followed created the PPC advertising system. Credit for the concept of the PPC model is generally given to Idealab and Goto.com founder Bill Gross.[12]
Facebook Ads and Instagram Ads take relevance and ad engagement into consideration. Ads that perform well are given a higher relevance score and are given more impressions at a cheaper price than ads with low relevance. Similarly, AdWords assigns ads a quality score based on factors like keyword relevance and landing page quality that can affect how much you pay for each click.
There are simple and fast random walk-based distributed algorithms for computing PageRank of nodes in a network.[31] They present a simple algorithm that takes {\displaystyle O(\log n/\epsilon )} rounds with high probability on any graph (directed or undirected), where n is the network size and {\displaystyle \epsilon } is the reset probability ( {\displaystyle 1-\epsilon } is also called as damping factor) used in the PageRank computation. They also present a faster algorithm that takes {\displaystyle O({\sqrt {\log n}}/\epsilon )} rounds in undirected graphs. Both of the above algorithms are scalable, as each node processes and sends only small (polylogarithmic in n, the network size) number of bits per round.
Provide full functionality on all devices. Mobile users expect the same functionality - such as commenting and check-out - and content on mobile as well as on all other devices that your website supports. In addition to textual content, make sure that all important images and videos are embedded and accessible on mobile devices. For search engines, provide all structured data and other metadata - such as titles, descriptions, link-elements, and other meta-tags - on all versions of the pages.

Nearly all PPC engines allow you to split-test, but ensure that your ad variations will be displayed at random so they generate meaningful data. Some PPC platforms use predictive algorithms to display the ad variation that's most likely to be successful, but this diminishes the integrity of your split-test data. You can find instructions on how to ensure that your ad versions are displayed randomly in your PPC engine's help section.
To answer the question 'What is digital marketing?', we have put together this new visual definition summarizing all the activities that form digital marketing that needs to be managed across the Smart Insights RACE Planning framework. It's used in the new, 6th edition of Dave's Digital Marketing book. We explain best practices for all of these in our Digital Marketing Elearning course.  The infographic is divided into activities to develop and manage digital strategy at the top to the marketing activities at the bottom.
Another excellent guide is Google’s “Search Engine Optimization Starter Guide.” This is a free PDF download that covers basic tips that Google provides to its own employees on how to get listed. You’ll find it here. Also well worth checking out is Moz’s “Beginner’s Guide To SEO,” which you’ll find here, and the SEO Success Pyramid from Small Business Search Marketing.