# Putting people into models Social networks and Bayesian networks Ingrid van Putten CSIRO – Marine and Atmospheric research (Hobart- Australia) What are.

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Putting people into models Social networks and Bayesian networks Ingrid van Putten CSIRO – Marine and Atmospheric research (Hobart- Australia) What are networks and what are social networks Where did it all start? Small world, random, and scale-free networks Jacopo A. Baggio School of Human Evolution &Social Change, Arizona State University Linking qualitative, networks and Bayesian networks How do Bayesian networks work? Fisheries example – quota trade market

Networks: How did it all start? Leonhard Euler (1707 – 1783) Commentarii Academiae Scientiarum Imperialis Petropolitanae, vol. 8, pp. 128-140, 1736 The problem, which I am told is widely known, is as follows: in Königsberg in Prussia, there is an island A, called the Kneiphof; the river which surrounds it is divided into two branches, as can be seen in the figure, and these branches are crossed by seven bridges, a, b, c, d, e, f and g. Concerning these bridges, it was asked whether anyone could arrange a route in such a way that he would cross each bridge once and only once.

Networks: How did it all start? Definitions (in modern words): A network is a figure of points (vertices/nodes/actors) connected by non-intersecting curves (edges/links/ties). A vertex is called odd if it has an odd number of arcs leading to it. An Euler path is a continuous path that passes through every arc once and only once. Theorems: If a network has more than two odd vertices, it has no Euler paths; if it has two or less odd vertices, there is at least one Euler path.

An arrangement of intersecting horizontal and vertical lines 1 a network of arteries WEB, lattice, net, matrix, mesh, crisscross, grid, reticulum, reticulation; Anatomy plexus. 2 a network of lanes MAZE, labyrinth, warren, tangle. 3 a network of friends SYSTEM, complex, nexus, web, webwork. [http://serialconsign.com/2007/11/we-put-net-network] What is a network? What is a SOCIAL network? A social structure that is made up of entities/ agents/ individuals/ or organisations that have ties/ relationships (interactions) between them. Ties or relationships could be anything …. Information exchange KinshipFriendship Market exchange Physical networks

The Blogosphere Biochemical networks Gene-protein networks Food webs: who eats whom The World Wide Web (?) Airline networks Call centre networks Paper citations Physical interaction networks Social interaction networks Friendships Acquaintances Boards and directors Organizations facebook.com twitter.com

Networks and Matrices node, vertex, actor link, edge, tie V = {v 1 …v n } Graph G(V,E) E = {e 1 …e n } 1 2 3 4 5 1 2 2 2 44 4 33 3 55 5 1 1 Directed Undirected Symmetrical Not symmetrical

How did interest in social networks start? The research was groundbreaking human society is a network characterized by short path (chain) lengths ……………. Six degrees of separation ………………… Stanley Milgram (and other researchers) carried out what is now known as “The small world experiment” The experiments are often associated with the phrase "six degrees of separation", although Milgram did not use this term himself.

CSIRO. Chain length ' 6.5 How did Milgram do the experiment? Information packets sent to "randomly" selected individuals around USA. Packets had basic information about a target contact person in Boston (Boston stockbroker). This person is the end destination for the packet. If the recipient personally knew the Boston stockbroker described in the letter, they should forward the letter directly. If they did not know the Boston stockbroker personally, then the person was to think of a friend or relative he knew personally who was more likely to know the target. Could only send to someone with whom they were on a first-name basis Recipient was directed to sign his name on a roster and forward the packet to the next person When and if the package eventually reached the contact person in Boston, researchers could examine the roster to count the number of times it had been forwarded from person to person 20% of packets reached target 1 2 3 4

CSIRO. John Guare wrote a play called Six Degrees of Separation, based on this concept. One of the main character’s lines (Quisa) “Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice… It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people…” Milgram’s experiment Chain length ' 6.5

Erdős Number (Bacon game for the scientist) Number of links required to connect scholars to Erdős, via co-authorship of papers Paul Erdős (1913-1996) Paul Erdős was an influential and itinerant mathematician (often living out of a suitcase boarding with his colleagues). He published more papers during his life (at least 1,525) than any other mathematician in history (with 507 co-authors) Jerry Grossman’s (Oakland Univ.) website allows mathematicians to compute their Erdos numbers: http://www.oakland.edu/enp/ http://www.oakland.edu/enp/ Connecting path lengths, among mathematicians only: average is 4.65 maximum is 13

Random Graphs --- or why does the “small world” phenomena exist? N = nodes (individuals) (A pair of nodes has probability p of being connected) (Average degree, k ≈ pN) p=0 ; k=0 N = 12 p=1.0 ; k≈N Each person is connected to two neighbours either side Takes three steps to get from A to B A B Now put in few random connections Number of steps to get from A to B reduced to two p= number of nodes with links N = 12 K=number of links

small-world network L = avg shortest path length C = avg clustering coefficient

Most networks are not random but are ‘scale free’ Tend to have a relatively few nodes of high connectivity (the “Hub” nodes – or “broker” nodes) Our world complies with the Pareto principle (also known as the 80–20 rule, the law of the vital few)

Degree Distribution & Power Laws Many real-world networks exhibit a power-law distribution (also called “Heavy tailed” distribution) Albert and Barabasi (1999) Power laws in real networks: (a) WWW hyperlinks (b) co-starring in movies (c) co-authorship of physicists (d) co-authorship of neuroscientists (e) Distribution of wealth Power-law distributions are straight lines in log- log space P(k) (k) Number of nodes with k links Number of links Lots of nodes with only a few links

CSIRO. Power Laws ….. Scale-Free Networks

Power Laws ….. What happens if you take out a few hubs? Take out 9 centres Take out 7 centres – but target the hubs

Structure matters: Power law versus random networks Epidemic spreading Structure matters: what do we know? - Structural properties influence a system strengths and weaknesses. - Structural properties influence diffusion processes such as viruses, pests, communication, information, migration and so on. - There is no golden rule (the “perfect” structure for all systems does not exist)

Australian fisheries example of network analysis: Lease quota trade for lobsters Industry structural change after tradeable quota introduced

1999 (year after the introduction of quota) New relationships – more brokers / hubs 2007 (8 years later) Mapping the lease quota trade (each line is a trade between two individuals)

Investor Independent fisher Lease quota dependent fisher Quota redistributor Income supplementer Lease market network Active fishers

Independent fishers (A-C) Van Putten (2011) A B CD 25 Investors (A-D) 75 Income supplementers (A-C-D) Lease dependent fishers (A-B-C) Quota redistributors (A-B-C-D) Fishing effort (number of quota units fished) Ownership characteristics (number of quota units owned by fisher) Concentration of ownership Portfolio investors

Putting people into models Social networks and Bayesian networks Ingrid van Putten CSIRO – Marine and Atmospheric research (Hobart- Australia) Jacopo A. Baggio School of Human Evolution &Social Change, Arizona State University Linking qualitative, networks and Bayesian networks How do Bayesian networks work?

N2N1 N3 Qualitative models p2 p1 p3 Network models i2 i1 i3 undirected directed Road between power station 1- 2, and 1-3, but not between 2-3 Individuals 1-3 are friends with each other, and 1 is friends with 2, but 2 doesn’t feel like 1 is their friend and 2-3 are not friends at all Animal 3 experiences external factors that limit it (self effect). Animal 1 has a positive effect on animal 2, and animal 2 also has a positive effect on animal 3, but animal 2 has no effect on animal 1 (commensalism) ++ - Bayesian models Cold (1) Flu (2) Fever (3) If you have a cold (1) there is a chance you have a fever (3), and if you have the flu (2) there is also a chance you have a fever Conditional probabilities Fever Cold True False 0.6 0.4 0 1 Fever Flu True False 0.7 0.3 0.1 0.9

the probabilities of A and B P(A) and P(B) and the conditional probabilities of A given B and B given A P(A | B) and P(B | A) Thomas Bayes (1701-1761) Bayes' theorem gives the relationship between Each node represents a random variable. Each node represents a variable A with parent nodes representing variables B 1, B 2,..., B n Each node is assigned a conditional probability table (CPT) A Bayesian network is a directed graph

Visit to Asia Tuberculosis or Cancer XRay Result Bronchitis Lung Cancer Smoking Dyspnoea (SOB) Example from Medical Diagnostics Network represents a knowledge structure between medical difficulties, their causes and effects, patient information and diagnostic tests Patient Information Medical Difficulties Diagnostic Tests Diagnosis

CSIRO. Visit to Asia Tuberculosis or Cancer XRay Result Bronchitis Lung Cancer Smoking Dyspnoea (SOB) Example from Medical Diagnostics Bronchitis Medical Difficulties Tub or Can True False Bronchitis Present Absent Present Absent Present 0.90 0.70 0.80 0.10 Absent 0.l0 0.30 0.20 0.90 Dyspnea

CSIRO. Visit to Asia Tuberculosis or Cancer XRay Result Bronchitis Lung Cancer Smoking Dyspnoea (SOB) Example from Medical Diagnostics

We know the person has been to Asia From P=1.04 From P=6.48 From P=11.0 From P=43.6 We have some information about the patient Predictive reasoning Given evidence about a cause, what are the predicted effects (e.g. you know the person has been to Asia what is the probability that they have tuberculosis?)

X-ray results are normal …. We also can now see the x ray results are normal Increases the probability that it’s not tuberculosis or cancer Diagnostic Given evidence about an effect (symptom) how does this change our beliefs in the causes? (e.g. I observe there is nothing abnormal about the x-ray– how does that the affect the probability that it’s tuberculosis or cancer?)

Australian fisheries example of BBN: Torres Strait (between Papua New Guinea and far northern Australia)

Australian Examples: Torres Strait Pre-season surveyLobster abundance Non-indigenous commercial catch SEC fishery Papuan Private freezer Functional Island freezer Regional Authority (\$) Community business knowledge Community role models Working age men Hookah ownership Fuel costs Fishing costs Season Exchange rate Other lobster available Weather Ease of catching lobster Price live Price tails Social capital Crew availability Returns from fishing Full time fisher Part time fisher Casual fisher Incidental household payments Tradition & culture Government employment scheme Full time alternative income Cost related drivers Profit drivers Socio-cultural drivers Price related drivers

Pre-season surveyLobster abundance Non-indigenous commercial catch SEC fishery Papuan Private freezer Functional Island freezer Regional Authority (\$) Community business knowledge Community role models Working age men Hookah ownership Fuel costs Fishing costs Season Exchange rate Other lobster available Weather Ease of catching lobster Price live Price tails Social capital Crew availability Returns from fishing Full time fisher Part time fisher Casual fisher Incidental household payments Tradition & culture Government employment scheme Full time alternative income Cost related drivers Profit drivers Socio-cultural drivers Price related drivers  Objective: more full time indigenous fishers (use olympic quota, ITQ, community quota ?)  Assumed: economic drivers = key  Actually: socio-cultural & infrastructure Australian Examples: Torres Strait

Pre-season surveyLobster abundance Non-indigenous commercial catch SEC fishery Papuan Private freezer Functional Island freezer Regional Authority (\$) Community business knowledge Community role models Working age men Hookah ownership Fuel costs Fishing costs Season Exchange rate Other lobster available Weather Ease of catching lobster Price live Price tails Social capital Crew availability Returns from fishing Full time fisher Part time fisher Casual fisher Incidental household payments Tradition & culture Government employment scheme Full time alternative income Cost related drivers Profit drivers Socio-cultural drivers Price related drivers  Full time fishers − Economics (profit) is a driver − Social capital important too (crew, freezers) Australian Examples: Torres Strait

Full time alternative income Pre-season surveyLobster abundance Non-indigenous commercial catch SEC fishery Papuan Private freezer Functional Island freezer Regional Authority (\$) Community business knowledge Community role models Working age men Hookah ownership Fuel costs Fishing costs Season Exchange rate Other lobster available Weather Ease of catching lobster Price live Price tails Social capital Crew availability Returns from fishing Full time fisher Part time fisher Casual fisher Incidental household payments Tradition & culture Government employment scheme Cost related drivers Profit drivers Socio-cultural drivers Price related drivers  Part time fishers − Socio-cultural is key − Ease of access vs other income Australian Examples: Torres Strait

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