# PageRank Algorithm ## What is the PageRank Algorithm? - The **PageRank algorithm** is a fundamental component of search ranking systems - Originally developed by Larry Page and Sergey Brin, the founders of Google - **Widely adopted**: Many search engines rely on PageRank to help order search results - **Purpose**: Evaluates and ranks web pages based on their perceived relevance and importance - **Impact**: Pages considered more important (often because they receive links from other high-quality pages) rank higher in search results

PageRank is an algorithm that assigns a numerical weighting to web pages to measure their relative importance within a network of linked pages

## Why is the PageRank Algorithm Important? - Created to **tackle the difficulty of determining page importance** given the immense amount of information available on the web - Designed to **provide better search results** that are more precise and relevant by considering factors beyond simple keyword matching - Without ranking algorithms, search engines would struggle to present the most useful results first - Helps users find authoritative and trustworthy information more efficiently ## Key Elements of the PageRank Algorithm There are **4 key elements** to the PageRank algorithm: 1. Link analysis 2. Link weight distribution 3. Iterative calculation 4. Damping factor ### Link Analysis - The PageRank algorithm **analyses the structure of links between pages** on the web - Web pages are assigned importance based on the **quantity and quality of inbound links** from other pages - Each link acts as a **"vote"** for the target page, with the voting weight determined by the importance of the linking page - Pages with more high-quality links pointing towards them are deemed **more valuable and relevant**, receiving a higher weight - Pages with a higher weight score more highly and achieve a higher ranking in search results

Think of links as endorsements - a link from an authoritative source carries more weight than one from an unknown page

### Link Weight Distribution - The importance of a webpage is calculated by PageRank based on the total number of "votes" it receives - The algorithm **distributes a page's importance** to the pages it links to by sharing a portion of its importance with each outgoing link - Through this process, **high-quality pages are given greater importance** and make a larger impact in determining the ranking of other pages - If a page links to many other pages, each outgoing link receives a smaller share of that page's importance | Scenario | Weight Distribution | |----------|---------------------| | Page A (weight 1.0) links to 2 pages | Each linked page receives 0.5 weight | | Page A (weight 1.0) links to 10 pages | Each linked page receives 0.1 weight | | Page B (weight 0.5) links to 5 pages | Each linked page receives 0.1 weight | ### Iterative Calculation - The PageRank algorithm uses a **repetitive calculation process** - At the beginning, every webpage is given the **same initial value** to start with - In subsequent iterations, the significance of each page is **re-evaluated** by considering the weighted impact of inbound links - The process **continues until the rankings become stable** (converge to steady values) - This iterative approach ensures that the importance of all pages in the network is properly accounted for ### Damping Factor - The **damping factor** is a value between $0$ and $1$ (usually $0.85$) - Represents the **probability that a user will not follow a link** on a page and will instead jump to a random new page - Prevents the algorithm from getting stuck in infinite loops and makes the model more realistic - Models actual user behaviour - users don't always click links, sometimes they start fresh with a new search

The damping factor of $0.85$ means there's an 85% chance a user follows a link and a 15% chance they jump to a random page

## Factors Influencing PageRank Although the initial PageRank algorithm mainly concentrated on link analysis, present-day search engines consider **many factors** to improve search results rankings. These factors include: - Relevance - User engagement - Authority and trust - Content freshness - Mobile-friendliness ### Relevance - The **content of a web page** is a crucial factor in determining its ranking in search results - Influenced by the **keywords used**, the **quality of the content**, and **how relevant it is** to the search query - PageRank works in conjunction with content analysis to deliver the most appropriate results ### User Engagement - User interaction with a website can be measured through metrics like: - **Click-through rates** (CTR) - **Time spent on a page** (dwell time) - **Bounce rates** - These metrics reveal the **level of user engagement** - Pages that receive greater engagement from users may be **deemed more valuable** and rank higher ### Authority & Trust - The **reputation and authority** of a webpage or website play a crucial role - Several factors can enhance a website's ranking: - **Age of the domain** (older domains may be more established) - **Quality backlinks from reputable sources** (e.g., government websites, educational institutions, established news organizations) - **Trustworthy content** (accurate, well-researched information)

A link from a university website (.edu) or government site (.gov) typically carries more authority than a link from a personal blog

### Content Freshness - Search engines value **fresh and up-to-date content** - Search queries may give **priority to web pages that are frequently updated** or have recent information - Particularly important for time-sensitive topics like news, events, or current affairs - Websites that regularly publish new content may see ranking benefits ### Mobile-Friendliness - As mobile devices became more prominent, search engines started to **factor in mobile compatibility** when determining rankings - Major search engines primarily use the **mobile version of a site's content** to rank pages from that site - Having a **responsive design** and **optimizing the user experience on mobile devices** can have a positive impact on rankings - Mobile-first indexing means the mobile version of your site is now the primary version ## Limitations & Evolving Nature - Although the PageRank algorithm is important in search engine rankings, it is **not the only factor** that determines them - Search engines use **different algorithms and factors** to guarantee they provide varied, relevant, and high-quality search outcomes - Over time, the **details of the PageRank algorithm have undergone changes** - Search engines regularly **enhance their ranking methods** to cater to new challenges and meet user expectations - The algorithm must adapt to prevent manipulation (e.g., link farms, paid links)

PageRank is just one component of modern search ranking - hundreds of signals are now used to determine page rankings

## How Does PageRank Work? To illustrate how PageRank works, imagine an **academic citation network** where: - Each **research paper represents a page** - Each **citation from one paper to another represents a link** between pages ### The Citation Network Analogy **Main principles PageRank uses:** - The **number of citations a paper receives** (equivalent to the number of links a page gets) - The **importance of a paper** is determined by how many citations it receives AND by how prestigious the papers are that cite it - The **PageRank of each paper gets updated** every time it receives a new citation - This continues as the citation network grows ### Numerical Rating Based on Citations In the citation network: 1. Papers start with an equal initial ranking value 2. When Paper A cites Paper B, some of Paper A's importance is transferred to Paper B 3. If Paper A is highly cited (high importance), its citation of Paper B carries more weight 4. The more citations a paper receives from important papers, the higher its own ranking becomes **Example values after several iterations:** | Paper | Citations Received | PageRank Score | |-------|-------------------|----------------| | Paper 1 | Cited by Papers 3, 7, 11 | 0.468 | | Paper 2 | Cited by Papers 1, 5 | 0.138 | | Paper 3 | Cited by Papers 1, 2, 8 | 0.136 | | Paper 4 | Cited by Paper 11 | 0.124 | | Paper 5 | Cited by Paper 3 | 0.114 | - As more citations are made, the **PageRank of each paper undergoes changes** - As a result, the **PageRank of every paper they cite will also be altered** - The **number represents each paper's PageRank** - the higher the number, the more important - Once the network stabilizes, papers can be **ranked to determine the most influential** ones ### Sorted by Rating After the algorithm converges, papers can be sorted by their PageRank score: 1. **Paper 1** - 0.468 (most influential) 2. **Paper 2** - 0.138 3. **Paper 3** - 0.136 4. **Paper 4** - 0.124 5. **Paper 5** - 0.114 This ranking helps researchers identify the most significant papers in a field, just as PageRank helps search engines identify the most important web pages.

In the exam, you won't be asked about the algorithm specifically or its mathematical formula, just the overall concept of how it works through link analysis and iterative calculation

## Key Takeaways - PageRank revolutionized web search by introducing **link-based importance ranking** - The algorithm treats **links as votes of confidence**, with votes from important pages counting more - **Iterative calculation** ensures all pages in the network are properly evaluated - The **damping factor** prevents infinite loops and models realistic user behavior - Modern search engines combine PageRank with **many other factors** (content quality, user engagement, freshness, etc.) - The algorithm continues to **evolve** to combat manipulation and improve result quality