Linked: How Everything Is Connected to Everything Else and What It - - PowerPoint PPT Presentation

Linked: How Everything Is Connected to Everything Else and What It Means

Barabási, Albert-László

Büşra Alptekin, Jyrki Junnila, Jussi Jääoja, Johanna Nuotio, Petra Reimi

About the Book

• Networks are present everywhere – all we need is an eye for them
• The book shows how our thinking of networks has evolved, how networks

emerge and what they look like

• From the world of random networks into scale-free networks and complex

systems

Reductionism

= A complex system is nothing but the sum of its parts

• We are close to knowing just about everything about the pieces, but we’re far

from understanding nature as a whole

• We have taken apart the universe but have no idea how to put it back together
• Reassembly was harder than expected
• The laws of self-organization are still largely mystery to us
• Scientists have only recently been learning to map our interconnectivity

Königsberg Bridges, 18th century

• Can one walk across the

seven bridges and never cross the same one twice?

• L. P. Euler solved the

problem seeing the bridges as a graph, a collection of nodes and links

• Euler’s graph theory is the

basis for our thinking about networks

The Random Universe

• Erdős–Rényi model: theory of random networks, 1959->
• The simplest way to create a network was to play dice -> nodes connect

randomly

• Complexity equals to randomness
• We had no alternative for describing our

interlinked systems, so random networks came to dominate our ideas

• Now we know better: random networks

played little role in assembling our universe

Six Degrees of Separation

• Karinthy 1929: people are connected by five links (friend of a friend)
• Rediscovered in 1967 by Stanley Milgram
• studied the distance between two people in the US
• the median number of intermediate persons was 5.5
• On the Web (connecting people), any document is only 19 clicks away from

any other

• The Internet (connecting computers) has a separation of ten
• Now, the shrinking world brings down the degrees of separation -> maybe

closer to 3 these days

• We live in “a small world” because the society is a dense web

Small Worlds

• Mark S. Granovetter: The Strength
• f Weak Ties (1973)
• Weak social ties are more important than

strong friendships

• e.g. job hunting
• Society is structured into highly

connected clusters, in which everybody knows everybody else. A few external links are our bridge to the outside world.

Small Worlds

• The stronger the tie between two people, the larger the overlap between their

circle of friends -> clustering coefficient (Watts and Strogatz)

• how closely knit your circle of friends is (1.0 = all know each other, 0 = only one mutual friend)

Simple clustering: People live in a circle where everyone knows their immediate neighbours -> no small world Adding links: Now we have links to distant people around the globe; connecting nodes on the

• pposite sides

collapse the separation between all nodes

HUBS and CONNECTORS

Test to measure how social you are. People are asked to give yourself a point if you know anybody with given name in the list of 248 surnames from Manhattan phone book. Results: *few high scores in every social group-the law of few “Sprinkled among every walk of life, in other words, are a handful of people with a truly extraordinary knack of making friends and

• acquaintances. They are Connectors.”

Sample Average Range

College students (mostly immigrants): 21 2-95 White,high-educated academics 39 9-118 Homogeneous group Not given 16-108

• Bacon Game
• Nodes=>actors
• Links =>movies
• Average distance:3links
• Hubs=>well connected actors

Ex: John Carradine with 4000links

Bacon’s average distance from anyone 2.79, while Rod Steiger has 2.53links

https://oracleofbacon.org/

• If Hollywood forms a random network, Rod Steiger doesn’t exist with

probability of well connected actor ~10^(-120)

• Hollywood, society, Web are not unique by any means like Erdos and

Renyi theory.

• Hubs=>
• dominate structure of all networks
• Create short paths between any two nodes in large systems
• While average distance between two person is 6 (six degree of

separation), with connectors distance will be 1 or 2.

http://www.biodiscoveryjournal.co.uk/Archive/Media/A32Figure-2.jpg

THE 80/20 RULE

• Pareto’s Law or Principle=>Murphy’s Law of management
• 80%of profits are produced by only 20%of employees
• 80%of customer services problems are created by 20%of consumers
• 80%of crime is committed by 20%of criminals…
• 4/5 of our efforts are largely irrelevant
• 80%of links on the Web point to only 15% of Webpages
• 80%of citation go to 38% of scientists
• 80%of links in Hollywood are connected to 30% of actors

Random networks; National highway network Nodes => cities Links => highways

• Most nodes have

same number of networks

• No hubs

Scale-free networks Air traffic system Nodes=>airports

• Most nodes have a few

links

• A few highly connected

hubs exist

There are many small events but the numerous tiny events coexist with a few very large

• nes. These several hubs

define the network’s topology.

RICH GET RICHER

• Random model was based on two assumptions

1. All the nodes are available from beginning, number of nodes are fixed and stable. 2. All nodes are equivalent and linked randomly Discovery of hubs and the power law which describe hubs, destroy these assumptions. Real networks are not static, number of nodes in network grows.

Real networks have two laws:

• 1. Growth: number of nodes

increases in time. Web emerged

• ne node at a time and grow node

by node.

• 2. Preferential attachment: it is more

likely that new nodes will connect to the more connected one.

• Web pages with more links are

more likely to be visited again

• Highly connected actors are more

likely to get new roles

• Highly cited papers are more likely

to be cited again…

Einstein’s Legacy

• The basic prediction: first mover has an

advantage

• However, in competitive environment

fitness also plays a role

• Networks fall into two categories:

○ fit-get-rich ○ winner-takes-all

• Einstein’s prediction of a new form of

matter: Bose-Einstein condensate → winner-takes-all behaviour

http://www.just911cars.com/wp-content/uploads/2016/10/Pirelli-Road-America-2.jpg https://upload.wikimedia.org/wikipedia/commons/9/9b/Einstein_gyro_gravity _probe_b.jpg

Achille’s Heel

• Interconnected systems are

efficient, but vulnerable

• How long will it take a network

to break into pieces once we randomly remove nodes?

• Cascading failures

https://upload.wikimedia.org/wikipedia/commons/3/3f/Internet_map_1024_-_transparent,_inverted.png

Viruses and Fads

Spread of fads, ideas, and epidemics in complex networks resemble each other

• The bell curve:

What is the role of social network in the spread of a virus or an innovation?

https://media.licdn.com/mpr/mpr/AAEAAQAAAAAAAAjcAAAAJDYxZ DE3NWRkLWM3YjAtNDBkMS1hNzhmLWRhOTMyZDcwZGU4MA.jp g

The Awakening Internet

• the development of the Internet is at first based on the demand of army
• Paul Baran found (in 1964) three

possible topologies for the

• ptimal structure of the Internet:

centralized, decentralized and distributed network

• the ideal structure would be

distributed network

• while the Internet is human

design, it now lives a life of its own

The Fragmented Web

• the knowing of the Internet’s topology is very important
• the best search engines’ coverage is only 15 %
• it’s only 19 step from World Wide Web’s edge to another edge
• some links are only one direction
• the Web is full of disjointed paths and they determine

the navigability of the Web

• the Web is divided into four

major continents: Central Core, IN Continent, OUT Continent, and Islands and Tendrils

• all directed networks break

into the same four continents

The Fragmented Web

Networks in Economy

Corporation structure from tree to web or network organization Director network held together by directors in multiple boards (21 %)

• Prefer well connected and experienced directors

Labour moves between companies - Silicon Valley Intricate and interlocked network nature => complex social and power networks “A hierarchy of well connected large companies brought together a large number

• f small companies, seamlessly integrating all players into an evolving scale-free

economy.”

Network Economy

Market is a directed network in reality. Buyers and suppliers are partners. Network thinking: monitor path of the damage, to set firewalls and strengthening nodes. Network Economy needs each node to be profitable.

• Strategic alliances and partnerships essential
• Globalization
• Management revolution

Products and ideas spread by highly connected hubs

Web Without a Spider

Real networks are not static or as random as thought before:

• growth
• not centralized
• hubs have a hierarchy, no single all important node
• self-organized

Each time nature spins a new web, fundamental structural features exist in webs spun before. Understanding complexity, what happens along the links?

• Network is just a skeleton

Hierarchies and Communities

First complex systems late 1990s:

• Scale-free networks => paradigm shift that webs are far from random
• web first one to examine

Networks infect different areas of human inquiry => research on properties of complex networks Complex systems

• Multitasking is an inherent property
• Modularity, not shown in the scale-free network or the random network model

○ Real networks are modular

Hierarchical Network

• Hierarchical clustering = generic

property of real networks

• Hierarchical modularity, parts of a

system can evolve separately => multitasking and hub coordination

Networks and complexity

Link between networks and theory of complexity Networks prerequisite for describing complex systems.

http://www.earthdecks.net/complexity/

Thank You!