# 231111202027 - Network Theory and Graphs ## 📝 Summary Network theory, a part of graph theory—a field of mathematics, involves studying relationships between entities. It is widely used in various fields like biology, computer science, social sciences, and physics. A graph consists of nodes (or vertices) and edges (or links) representing entities and relationships. Network theory also has advanced concepts, such as dynamic networks, multilayer networks, and network resilience. Various tools and techniques are deployed for graph visualization and computational network analysis. ### ☝️ Key points - The basics of Graph Theory involve understanding nodes, edges, and different types of graphs. - Network theory has many concepts: degree, paths, cycles, network topology, clustering coefficient, and centrality measures. - Applying network theory can be seen in social networks, biology, technology, physics, economics, and finance. - Advanced topics in network theory include dynamic networks, multilayer networks, and network resilience. - Tools like Gephi or NetworkX are used for graph visualization, while computational analysis involves algorithms for finding shortest paths, detecting communities in networks, etc. ## 📑 Content ### Basics of Graph Theory #### Nodes and Edges In graph theory, a 'graph' consists of 'nodes' (or vertices), representing entities, and 'edges' (or links) connecting these nodes, representing their relationships or interactions. #### Types of Graphs Graph types include undirected, directed, and weighted graphs. ### Concepts in Network Theory Network theory encompasses many concepts like degree, paths, cycles, network topology, clustering coefficient, and centrality measures, which offer a whole picture of any network. ### Applications of Network Theory Network theory has extensive applications across multiple disciplines, including social networks, biology, technology, physics, economics, and finance. ### Advanced Topics Dynamic Networks, Multilayer Networks, and Network Resilience are complex concepts that build upon the basics of network theory. ### Tools and Techniques Graph Visualization and Computational Analysis are crucial components in the practical application of network theory. ```mermaid graph TD; A[Nodes]-->B[Edges]; B-->C[Undirected Graphs]; B-->D[Directed Graphs]; B-->E[Weighted Graphs]; ``` Diagram description: This mermaid diagram demonstrates the basic components of graph theory, starting from nodes connecting to edges, further detailed into different types of graphs - Undirected, Directed, and Weighted Graphs. ## 🎓 Resources - David Easley and Jon Kleinberg's [Networks](http://www.cs.cornell.edu/home/kleinber/networks-book/) book, a comprehensive guide to network theory. - [Network Science](http://networksciencebook.com/), an online course by Albert-László Barabási. - [Introduction to Network Theory](https://www.coursera.org/lecture/algorithms-graphs-data-structures/introduction-to-network-theory-7IJDP) Coursera course <iframe width="560" height="315" src="https://www.youtube.com/embed/09_LlHjoEiY?si=Q4R5XJ5H_yMOvEr_" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen></iframe> ## 🔗 References - NE Newman's [The structure and function of complex networks](https://arxiv.org/abs/cond-mat/0303516) research paper - [Graph Theory](https://en.wikipedia.org/wiki/Graph_theory) on Wikipedia ### Further reading - [A Guided Tour of Network Theory](https://www.amazon.com/A-Guided-Tour-of-Network-Theory/dp/0262015848) - Douglas Luce & Perry Pangaribuan - [Networks, Crowds, and Markets: Reasoning About a Highly Connected World](https://www.amazon.com/Networks-Crowds-Markets-Reasoning-Connected/dp/0521195330) - David Easley & Jon Kleinberg ### Backlinks - [[231111202005 - Network Theory and Graphs Overview]] - [[Social Network Analysis]] - [[Graph Theory in Computer Science]] - [[Complex Networks in Biology]] - [[Network Models in Physics]] - [[Networks in Economics and Finance]] **🏷️ Tags:** #type/wiki #topic/network-theory #topic/graph-theory