PHYS 5116: Complex Networks | Fall 2019

**Course description and objectives**

The course is an interdisciplinary introduction to the emerging science of complex networks and their applications. Topics to be covered include the mathematics of networks (graph theory), data analysis, and applications to biology, sociology, technology, and other fields. Students will learn about the ongoing research in the field, and ultimately apply their knowledge to conduct their own analysis of a real network data set of their choosing as part of the final project.

**Course organization**

*Lectures:* Lectures will be given jointly by Prof. Barabási, by Drs. Towlson, Ruf, Danziger, and Shekhtman.

*Homework:* There will be three (3) homework assignments representing a mix of mathematical work and computational data analysis. Students are expected to turn in their source code for the computational exercises. Students in the Network Science Ph.D. program will typically be asked to do at least one, more challenging, problem on top of each assignment.

*Examinations:* Final project presentation — complete analysis of a real network. In place of a midterm exam, there will be an intermediate presentation to check your progress and provide feedback.

Lectures

04

Sep

We are surrounded by systems that are hopelessly complex, from the society, a collection of seven billion individuals, to communications systems, integrating billions of devices, from computers to cell phones. Our very existence is rooted in the ability of thousands of genes to work together in a seamless fashion; our thoughts, reasoning, and our ability to comprehend the world surrounding us is hidden in the coherent activity of billions of neurons in our brain.

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Sep

Networks and graphs: In its simplest form, a network is a set of nodes connected by links. A graph, however, is a set of vertices connected by edges? Do you sense the difference? Well, regarding the common usage of these terms, there is none: graph and networks these days are used interchangeably, and so do terms of nodes and vertices and links and edges.

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Sep

The first basic question we need to answer is the following: if you are given a network, how do you think of it? How do you model it? How do you describe them analytically? This is a particularly difficult question, particularly given the diversity of the networks we are facing in this discipline. Most important, it is difficult to understand how the position of the links are decided in a given networks—each network may have a different role for that.

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Sep

Many real world networks have a similar architecture: WWW, Internet (routers and domains), electronic circuits, computer software, movie actors, coauthorship networks, sexual web, instant messaging, email web, citations, phone calls, metabolic, protein interaction, protein domains, brain function web, linguistic networks, comic book characters, international trade, bank system, encryption trust net, energy landscapes, earthquakes, astrophysical network…

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