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An Introduction to Social Network Analysis Fulvio D’Antonio NARG: Network Analysis Research Group DII - Dipartimento di Ingegneria dell'Informazione Università Politecnica delle Marche 1

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Outline What is a social network? A little history… Modelling social networks with random graphs Link prediction Content-based social networks 2

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What is a Social Network? Networks in which nodes and ties model social phenomena. Generally represented using graphs Different kind of relationships: ◦ Static (kinship, friendship, similarity,…) ◦ Dynamic (information flow, material flow,…) 3

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History In the 19 th century Durkheim introduces the concept of “social facts” ◦ phenomena that are created by the interactions of individuals, yet constitute a reality that is independent of any individual actor. In the 1930s, Moreno: ◦ the systematic recording and analysis of social interaction in small groups, especially classrooms and work groups (sociometry) ◦ He invents the “sociogram” (graphical representation of interpersonal relationships) 5

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6 History (2): Milgram’s experiment (1960s) People in Nebraska, were each given a letter addressed to a target person in Boston, Massachusetts, along with demographic information (name, address, profession) on this person. They were asked to send the letter to the target person, by forwarding it to other people Average number of hops to get the letter to the target: 6 ◦ “six degrees of separation”

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History (3): The Strength of Weak Ties Granovetter ◦ “The Strength of Weak Ties” (1973) considered one of the most important sociology papers written in recent decades ◦ He argued that “weak ties” could actually be more advantageous in politics or in seeking employment than “strong ties” ◦ Some reasons: They allows you to reach a vaster audience. Information coming from weak ties is “fresh”

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Understanding Networks with Random Graphs A random graph is a graph that is generated by some random process The objective is to study the properties of random graphs (e.g. diameter, clustering coefficient, mean degree) Are generated graphs compatible with actual social networks? Different approaches: ◦ Erdős–Rényi Graphs ◦ Small-World model ◦ Barabasi-albert model 8

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Random Graphs Studied by P. Erdös A. Rényi in 1960s How to build a random graph ◦ Take n vertices ◦ Connect each pair of vertices with an edge with some probability p There are n(n 1)/2 possible edges The mean number of edges per vertex is

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Degree Distribution Probability that a vertex of has degree k follows binomial distribution In the limit of n >> kz, Poisson distribution ◦ z is the mean

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Characteristics Small-world effect (Milgram 60s) Diameter (Bollobas) Average vertex-vertex distance Grows slowly (logarithmically with the size) Doesn’t fit real-world networks Degree distribution (not Poisson!) Clustering (Network transitivity) Random graphs: small clustering coefficient social networks, biological networks in nature, artificial networks – power grid, WWW: significantly higher

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Clustering If A is connected to B, and B is connected to C, then it is likely that A is connected to C “A friend of your friend is your friend” The average fraction of a node’s neighbor pairs that are also neighbors each other

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Small-World Model Watts-Strogatz (1998) first introduced small world model Mixture of regular and random networks Regular Graphs have a high clustering coefficient, but also a high diameter Random Graphs have a low clustering coefficient, but a low diameter Characteristic of the small-world model The length of the shortest chain connecting two vertices grow very slowly, i.e., in general logarithmically, with the size of the network Higher clustering or network transitivity

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Small-World Model (2) 14 Construct a regular ring lattice. Each node has degree k For every node take every edge (a,b) with i < j, and rewire it with probability β

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Scale-Free Network A small proportion of the nodes in a scale-free network have high degree of connection Power law distribution A given node has k connections to other nodes with probability as the power law distribution with exponent ~ [2, 3] Examples of known scale-free networks: Communication Network - Internet Ecosystems and Cellular Systems Social network responsible for spread of disease

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Barabasi-Albert Networks Start from a small number of node, add a new node with m links Preferential Attachment Probability of these links to connect to existing nodes is proportional to the node’s degree “The rich gets richer” This creates ‘hubs’: few nodes with very large degrees

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Link Prediction Who will be connected in the next future (present or past)? Why link prediction? ◦ Eliciting hidden or Incomplete link information Missing links from data collection (criminal networks) ◦ Recommendation Friends, groups in social networks Product, Book, Movie, Music on e-commerce site Articles on content site Who should one collaborate? ◦ …. 17

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Ok, this was about the structure…. but what about the content? 18

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Content-based social networks A special kind of Social Networks The actors (nodes) of the network produce documents ◦ They can be produced by more than one actor co-authorship relationship Similarity relationship between any 2 actors A and B of the network can be estimated using a function on the set of documents produced Doc(A) and Doc(B) ◦ Sim: DOC(A) DOC(B) [0,1] 19

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Automatically detecting content-based social networks NLP Methodology*: 1. Choose a set of actors and gather related documents; 2. Pre-process textual data to extract raw text; 3. Process raw text with a part-of-speech tagger; 4. Extract candidate annotating terms by using a set of part- of-speech patterns 5. Rank candidates, possibly filter them choosing a threshold; 6. Output a set of weighted vectors V of annotating terms for each documents; 7. Group the vectors by actor and construct a centroid (i.e. a mean vector) with such groups. This centroid roughly represents the actor main interests. 8. Build a graph by computing a similarity function for each pair of centroids. *Cooperation with university of Rome 20

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Reducing Information Dimensionality: Clustering / Community finding dividing a set of data-points into subsets (called clusters) so that points in the same cluster are similar in some sense ◦ Crisp/Fuzzy clustering ◦ Partitive/Non partitive clustering K-means, repeated bisection, graph partitioning,… Cohesive subgroups detection: ◦ Cliques ◦ K-Cliques ◦ K-Plex ◦ Density based subgraphs 21

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Experiments: Research Networks INTEROP NoE (6FP): Domain Ontology expressed using OWL (Ontology Web Language) in the Interoperability of Software Application domain INTEROP partners’ corpus 2 types of edges: Coauthorship Similarity 22

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Evaluation: Research Networks Experiment 1: evaluation of the automatical research interests extraction Project members were asked to select a subset of concepts from the INTEROP ontology, in order to express their research interests (GROUND TRUTH) For each partner we compared the vectors (expanded or not) automatically extracted with the interests declared. Higher recall performance with vectors expansion but lower precision. Mean PrecisionMean recall Not Expanded Expanded

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Evaluation: predictive power of the model We evaluated how many of the possible opportunities computed for year 2003 have been exploited in the rest of the project ( ). Perc. of opportunities for year 2003 realized in the rest of the project ( ) Perc. of opportunities for year 2004 realized in the rest of the project ( ) YearPerc. realized In % In % After % YearPerc. realized In % After % 24

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Experiments: Patent Networks The European Patent Office (EPO): web-services to access to information about European patents that have been registered; the date of presentation the applicant name and mission, the address of the applicant textual description of the patent. 25

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Thank you….. Questions?!?!?! 26

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