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, 18 th 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 of 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) Adding links: Simple clustering: Now we have links to People live in a distant people around circle where the globe; connecting everyone knows nodes on the their immediate opposite sides neighbours -> no collapse the small world 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 Sample Average Range College students 21 2-95 (mostly immigrants): White,high-educated 39 9-118 academics Homogeneous group Not given 16-108 “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.”
•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 http://www.biodiscoveryjournal.co.uk/Archive/Media/A32Figure-2.jpg • 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.
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; Scale-free networks National highway Air traffic system network Nodes=>airports Nodes => cities • Most nodes have a few Links => highways links • Most nodes have • A few highly connected same number of hubs exist networks • No hubs There are many small events but the numerous tiny events coexist with a few very large ones. 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 one 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 http://www.just911cars.com/wp-content/uploads/2016/10/Pirelli-Road-America-2.jpg ● 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 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 optimal 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 Fragmented 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
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 of 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
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