Network Theory: Introduction

Learn the Language of Networks
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  • Lectures 26
  • Contents Video: 1.5 hours
    Other: 1 hour
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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About This Course

Published 4/2015 English

Course Description

Network theory is one of the most exciting and dynamic areas of science today with new breakthroughs coming every few years as we piece together a whole new way of looking at the world, a true paradigm shift that is all about connectivity. The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and computer science to almost all areas of social science.

From the metabolic networks that fuel the cells in our body, to the social networks that shape our lives, networks are everywhere, we see them in the rise of the internet, the flow of global air traffic and in the spread of financial crises, learning to model and design these networks is central to 21st century science and engineering.

This is an introductory course where we present topics in a non-mathematical and intuitive form that should not require any specific prior knowledge of science as the course is designed to be accessible to anyone with an interest in the subject. During the course we will explore all the major topics including:

Networks Overview: In this first section to the course we are going to give an overview to network theory that will also work as an overview to the structure of the course and the content we will be covering. We talk about what we called the network paradigm that is the whole new perspective that network theory offers when we look at the world through the lens of connectivity.

Graph theory: In this second section we lay down the basics of our language for talking about graphs by giving an introduction to graph theory, we talk about a node's degree of connectivity and different metrics for analyzing a nodes degree of centrality and significance within a network

Network Structure: In the third section we explore the overall topology to a network by talking about connectivity, that is how connected the whole network is, diameter, density and clustering all key factors in defining the overall structure to a network.

Types Of Networks: In this section we will be looking at different models to networks by starting out with a randomly generated network we will see how most network are in fact not random but have some distinct structure, here we will be talking about a number of different models such as centralized scale free networks and the small world phenomena.

Network Diffusion & Dynamics: In the last section to the course we touch upon how networks change over time, in particular looking at the different parameter affecting the generation of a network, how something spreads or fails to spread across it and finally wrap-up by talking about network robustness and resilience.

What are the requirements?

  • No prior knowledge of mathematical modeling or science is required before taking this course (although it would be of a bonus) all that is required is a good understanding of the English language

What am I going to get from this course?

  • By the end of taking this course you will have a solid grasp of the formal language of network theory, the standardized language used to model networks within a wide variety of domains
  • You will have a solid conceptual background required to approach a more advanced course in the mathematical analysis of networks

What is the target audience?

  • Being an introductory course it is design to be accessible to a broad group of people but will be of particular relevance to those in engineering, science (particularly the social sciences), mathematics or I.T.

What you get with this course?

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Curriculum

Section 1: Overview
05:49

In this first module we kick the course off by giving an overview to the different questions that we are interested in trying to answer when it comes to analysing networks, this module also works as an overview to the content we will be covering during the rest of the course.

06:58

In this module we started our discussion on networks to by looking at what we called the network paradigm, a paradigm is the set of methods and assumptions underlying a particular scientific domain as such it constitutes a whole way seeing the world.

6 pages

Quick review of what we covered in the previous video

Section 2: Graph Theory
04:21

In this lecture we start to lay down some of our basic language for talking about networks that comes to us from graph theory a relatively new area of mathematics that studies the properties of graphs

Lesson Summary
6 pages
04:19

In this module we start our discussion on one of the central concepts within network theory that of connectivity where we are interested in analysing the connections an individual node has

Lesson Summary
01:22
05:29

In this module we talk about one of the key concepts in network theory, centrality. Centrality gives us some idea of the nodes position within the overall network and it is also a measure that tells us how influential or significant a node is within a network although this concept of significance will have different meanings depending on the context.

Lesson Summary
6 pages
Section 3: Network Topology
05:38

We call the overall structure to a network its topology where topology simply means the way in which constituent parts are interrelated or arranged. To illustrate how network topology effects the system we look at a number of simple networks each containing the same amount of nodes but each having a different overall topology owing to the way they were connected with these topologies effecting different features to the network, such as the shortest path length or how we might control the flow of information on the network

Lesson Summary
7 pages
05:14

One of the defining features to a network is going to be its overall degree of connectivity, which might qualify as the defining feature. Going from a system with a low degree of connectivity to one with a high degree of connectivity is not just a quantitative change in the number of edges within the network it is also qualitative change as we will try to demonstrate in this short lecture.

Lesson Summary
6 pages
05:54

The size of a network is important not so much because of the sheer quantity of elements we are dealing with, but more because it sets the context for how close or far on average one node in the network is from another and this will tell us how quickly something will spread through the network and also how integrated different components in the network are likely to be.

Lesson Summary
6 pages
04:03

The way in which a network is connected plays a large part in how we will analyze and interpret it. When analyzing connectedness and clustering we are asking how integrated or fractured the overall network system is, how these different major sub-systems are distributed out and their local characteristics.


Lesson Summary
5 pages
Section 4: Network Models
04:19

In this module we introduce the concept of degree distribution as a key parameter in defining the type of network structure we will be dealing with. We show how by altering this metric we can generate different widely encountered models to networks.

05:51

In this module we continued on with our discussion about how different degree distributions within a network generate different network models this time looking at what we called decentralized networks, a structure that is discernibly different from the random graph that we started with.

06:46
In this module we talked about random graphs more formally termed the Erdős–Rényi random graph, where connections between nodes are placed at random with a given probability for their concurrence
Lesson Summary
6 pages
05:45

In this module we looked at networks that have the highest degree distribution making their topology very heterogeneous in terms of the distribution of connectivity, these networks may have one or a few nodes with a very high degree of connectivity forming global hubs within the network and very many with a much smaller degree of connectivity

Section 5: Dynamics & Diffusion
06:47

Almost all real networks are dynamic in nature and how they have evolved and change overtime is a defining feature to their topology and properties. As network theory is a very new subject much of it is still focused on trying to explore the basics of static graphs, as the study of their dynamics results in the additional of a whole new sets of parameters to our models and takes us into a new level of complexity, much of which remains unexplored, and is the subject of active research.

07:37

How something will spread across a network is a key question we will be interested in when analyzing many different networks, more formally we call this spreading on a network propagation or diffusion, this process of diffusion and is defined by a number of different parameters that we will be exploring in this module

08:06

Robustness and resilience are often defined in terms of a system's capacity to maintain functionality in the face of external perturbations. In this model we give an overview to network robustness looking at what happens when we remove links and node, both strategically and randomly

Section 6: Conclusion
Conclusion
4 pages

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Instructor Biography

Complexity Academy, eLearning for Complex Systems

Complexity Academy is an e-Learning site dedicated to the area of complex systems, our mission is to take the world of complexity and make it accessible to all. Complex systems can be an intimidating subject with many sophisticated concepts this is why we believe it is important to always start with the most essential, simplest elements of a subject making sure that students come away with a solid understanding of the core concepts behind each area. As Einstein said "Make everything as simple as possible, but not simpler"

Courses are curated and presented by Joss Colchester. Joss has extensive experience within the domain of complex systems both within academic research(mathematical modeling of complex system + network analysis) and has many years practical systems engineering experience(designing and developing complex web based information systems). He has a passion for taking abstract and complex concepts and making them concrete and accessible to as broad an audience as possible by combining clear and effective graphics with well structured course content.


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