Presentation on theme: ""Introduction in Social Network Analysis"— Presentation transcript:
1 "Introduction in Social Network Analysis "Introduction in Social Network Analysis. Theoretical Approaches and Empirical Analysis with computer-assisted programmes."Dr. Denis GruberState University of St. PetersburgFaculty of SociologyDAAD-Lecturer for Sociology
6 What is a network? Definition: „(...) a specific set of linkages among a defined set of persons with the additional property that the characteristics of these linkages as a whole may be used to interpret the social behavior of the persons involved.“ (Mitchell 1969:2)
7 What is Social Network Analysis? “(…) is based on an assumption of the importance of relationships among interacting units“ (Wasserman/Faust 2008:4)“(…) encompasses theories, models, and applications that are expressed in terms of relational concepts or processes” (Wasserman/Faust 2008:4)“(…) the unit of analysis in network analysis is not the individual, but an entity consisting of a collection of individuals and the linkages among them” (Wasserman/Faust 2008:5)Network methods focus on:Dyads (two actors and their ties)Triads (three actors and their ties)Larger systems (subgroups of individuals, or entire networks)Primary literature:Wasserman, Stanley / Faust, Katherine (2008): Social Network Analysis. Methods and Applications, Cambridge, University Press
8 Principles of Social Network Analysis Actors and their actions are viewed as interdependent rather than independent, autonomous unitsRelational ties (linkages) between actors are channels for transfer or “flow” of resources (either material or nonmaterial)Network models focusing on individuals view the network structure environment as providing opportunities for or constraints on individual actionNetwork models conceptualize structure (social, economic, political, and so forth) as lasting patterns of relations among actors(Wasserman/Faust 2008:4)
9 The Social Network Approach The world is composed of networks - not densely-knit, tightly-bounded groupsNetworks provide flexible means of social organization and of thinking about social organizationNetworks have emergent properties of structure and compositionNetworks are a major source of social capitalNetworks are self-shaping and reflexiveNetworks scale up to networks of networks
10 Overview about the development of Social Network Analsis 19301950/60Simmel:Soziologie sollte sich – statt den Inhalten – den Formen der Vergesellschaftung durch eben diese Wechselwirkungen widmen(Beziehungen zwischen Individuen rückten ins Zentrum)1933 Der Psychologen Moreno (der späteren Begründer des “Psychodramas”) stellt die Soziometrie (visuelle Darstellung von Beziehungen) erstmals als wiss. Methode auf einem Medizinischen Kongreß vor.1970(Scott 1991, 7)
11 Persönlichen Netzwerke und Gesamtnetzwerke Bei der Untersuchung von Gesamtnetzwerken ermittelt man nun zu jedem Akteur, ob Beziehungen zu jedem anderen Akteur der Menge bestehen oder nicht.Bei den persönlichen Netzwerken hingegen stellt man für jeden Akteur fest, mit welchen Akteuren Beziehungen der vorgegebenen Art bestehen.Gesamtnetzwerk: Persönliche Netzwerke:Man unterscheidet in der Netzwerkanalyse zwei verschiedene Arten von Netzwerken, die persönlichen Netzwerke und die Gesamtnetzwerke.A123456789A123456789
12 Which differences exist between a social network analysis and a non-network explanation? in non-network explanations the main focus is on: attributes of autonomous individual units, the associations among these attributes, and the usefulness of one or more attributes for predicting the level of another attributesocial network analysis:refers to the set of actors and the ties among themviews on characteristics of the social units arising out of structural or relational processes or focuses on properties of the relational system themselvesinclusion of concepts and information on relationships among units in a studythe task is to understand properties of the social (economic or political) structural environment, andhow these structural properties influence observed characteristics and associations among characteristicsrelational ties among actors are primary and attributes of actors are secondaryeach individual has ties to other individuals, each of whom in turn is tied to a few, some, or many others, and so on(Wasserman/Faust 2008: 6-9)
13 What is a Social Network? A set of nodes (e.g., people or organisations)A set of connections between nodes (e.g., friends, acquaintances, relatives)Social network analysis is ofteninterested in paths or chainscommunicating information
14 Fundamental Concepts in Network Analysis actorrelational tiedyadtriadsubgroupgrouprelationsocial network
15 Actor“discrete individual, corporate, or collective social units” (Wasserman/Faust 2008:17)Examples: people in a group, departments within in a corporation, public service agency in a city, nation-states in the world systemDoes not imply that they have volition or the ability to “act”
16 Relational tie Actors are linked to another by social ties A tie “establishes a linkage between a pair of actors”Example of ties in SNA (Wasserman/Faust 2008:17):Evaluation of one person by another (expressed friendship, linking, or respect)Transfers of material resources (business transactions, lending or borrowing things)Association or affiliation (jointly attending a social event, or belonging to the same social club)Behavioral interaction (talking together, sending messages)Movement between places or statuses (migration, social or physical mobility)Physical connection (a road, river, or bridge connecting two points)Formal relations (authority)Biological relationships (kinship or descent)
17 Dyad a tie between two actors “consists of a pair of actors and the (possible) tie(s) between them” (Wasserman/Faust 2008:18)Shows “properties of pairwise relationships, such as whether ties are reciprocated or not, or whether specific types of multiple relationships tend to occur together” (Wasserman/Faust 2008:18)
18 Triad“Triples of actors and associated ties” (Wasserman/Faust 2008:19)“a subset of three actors and the (possible) tie(s) among them” (Wasserman/Faust 2008:19)Triadic analyses focus on the fact whether the triad isTransitive : if actor i “likes” actor j, and actor j in turn “likes” actor k, then actor i will also “like” actor kBalanced: if actors i and j like each other, then i and j should be similar in their evaluation of a third actor, k, and i and j dislike each other, then they should differ in their evaluation of third actor, k
19 SubgroupSubgroup of actors is defined “as any subset of actors, and all ties among them” (Wasserman/Faust 2008:19)
20 Group“is the collection of all actors on which ties are to be measured” (Wasserman/Faust 2008:19)Actors in a group “belong together in a more or less bounded set (…) consists of a finite set of individuals on which network measurements are made” (Wasserman/Faust 2008:19)“The restriction to a finite set or sets of actors is an analytic requirement. Though one could conceive of ties extending among actors in a nearly infinite group of acts, one would have great difficulty analyzing data such a network. Modeling finite groups presents some of the more problematic issues in network analysis, including the specification of network boundaries, sampling, and the definition of group. Network sampling and boundary specification are important issues.” (Wasserman/Faust 2008:19f.)“however, in research applications we are usually forced to look at finite collections of actors and ties between them.” (Wasserman/Faust 2008:20)
21 Relation“the collection of ties of a specific kind among members of a group” (Wasserman/Faust 2008:20)Example: the set of friendship among pairs of children in a classroomFor group of actors, several different relations might be measured“refers to the collection of ties of a given kind measured on pairs of actors from a specified actor set” (Wasserman/Faust 2008:20)Ties themselves only exist between specific pairs of actors
22 Social network“consists of a finite set or sets of actors and the relation or relations defined on them. The presence of relational information is a critical and defining feature of a social network.” (Wasserman/Faust 2008:20)“A social network arises when all actors can, theoretically, have ties to all relevant actors” (Wasserman/Faust 2008:42)
23 Work data sets What are network data? Boundary specification and samplingTypes of networks
24 What are network data?variablesmodesaffiliation variables
25 Variables (Wasserman/Faust 2008:29) structural variables: are measured on pairs of actors and are the cornerstone of social network data setsmeasure ties of a specific kind between pairs of actorsexample: business transaction between corporations, friendship between people, trade between nationscomposition variables:measurements of actor attributes (actor attribute variables)are of the standard social and behavioral science varietydefined at the level of individual actorsexample: gender, race, ethnicity for people
26 Modes“the number of sets of entities on which structural variables are measured” (Wasserman/Faust 2008:35)One-mode network: all actors come from one settwo-mode network: there are two set of actors: e.g. set consisting of corporations and another of non-profit organizations, contains measurements on which actors from one set have ties to actors from the other sethigher-mode network: more set of entities: actors from different sets
27 Affiliation Variables each affiliation variable is defined on a specific subset of actorsa special type of two-mode network, but they only have one set of actorsthe second mode is a set of events: such as clubs or voluntary organizations to which the actor belong“events are defined not on pairs of actors, but on subsets of actors (…) often events are informal social occasions, such as parties or other gatherings, and observations or attendance or interactions among people provide the affiliation of the actors ”“subsets can be of any size”
28 Boundary specification and sampling I What is your Population? (Wasserman/Faust 2008:31)Who are the relevant actors?Example: faculty in an academic department or corporations headquartered in a major metropolitan area: relatively easy to deal withBut what to do in other cases if the boundary of the set of actors may be difficult if not impossible to determine“The boundary of a set of actors allows a researcher to describe and identify the population under study”Actor set boundaries are often based on the relative frequency of interaction, or intensity of ties among members as contrasted with non-members
29 Boundary specification and sampling II Two different approaches to boundary specification in social network studies (cf. Laumann, Marsden, Prensk 1989)Realist approach: focuses on actor set boundaries and membership as perceived by the actors themselves (e.g. a street gang, members acknowledge as belonging to the gang)Nominalist approach: based on the theoretical concerns of the researcher (e.g. flow of computer messages among researchers in a scientific community; the list of actors might be the collection of people who published papers on the topic in the previous five years)In several applications, when the boundary is unknown, special sampling techniques such as snowball sampling and random nets(Wasserman/Faust 2008:32)
30 Boundary specification and sampling III: Sampling sometimes it is not possible to take measurements on all actors in the relevant actor set (Wasserman/Faust 2008:33)is seen as “representative of the larger, theoretically interesting population (which must have a well-defined boundary and hence, a known size), and uses the sampled actors and data to make inferences about the population)example:snowball network sample (cf. Goodman 1961): “begins when the actors in a set of sample respondents report on the actors to whom they have ties of a specific kind” (Wasserman/Faust 2008:34)all of the nominated actors constitute the “first order “ zone of the networkthen all actors in this zone will be sampled and all the additional actors (those nominated by the actors in the “first order” zone who are not among the original respondents or those in this zone) are gatheredthese additional actors constitute the “second order” zoneit is a chain method what means that several “order zones” can be defined
31 "Introduction in Social Network Analysis "Introduction in Social Network Analysis. Theoretical Approaches and Empirical Analysis with computer-assisted programmes."II. meeting:Types of networks for SNAFrom organic solidarity (Durkheim) to information society and network society (Castells)Social capital and social networksQuiz
32 Social Network Analysis: Focus on interactions between individuals/ groups Node: Any entity ina network(person, system,group, organization)Tie: Relationship/ interactionbetween two nodes.
33 Sociology of networksbeware – network analysis takes very distinct forms!sociometryMoreno (psychotherapy)graph theoryWhite (mathematical sociology)social capitalBourdieu (social theory)‘strength of weak ties’Granovetter (new ec sociology)networkssocial exclusionPhillipson (social policy)network cultureTerranova (cultural studies)network societyCastells (social theory)
34 Types of networksNetwork can be categorized by the nature of the sets of actors and the properties of the ties among them“The number of modes in a network refers to the number of distinct kinds of social entities in the network” (Wasserman/Faust 2008:35)One-mode networks: a single set of actorsTwo-mode networks: focus on two sets of actors, or one set of actors and one set of events
35 One-mode networks: a single set of actors (Wasserman/Faust 2008:36f.) What is important inside?actorsrelationsactor attributes
36 Actors in one-mode networks can be a variety of typesPeopleSubgroups (consist of peopleOrganizationsCollectives / Aggregates: Communities (consists of subgroups of people), nation-states (larger entities, containing many organizations and subgroups)
37 Relations in one-mode networks (Wasserman/Faust 2008:37) individual evaluations: friendship, linking, respect “measurements of positive or negative affect of one person for another”transactions or transfer of material resources: lending or borrowing; buying or selling, contacts made by one actor of another in order to secure valuable resources, transfer of goods, social support tiestransfer of non-material resources: communications, sending/receiving information frequently communications between actors, where ties represent messages transmitted or information receivedinteractions: physical interaction of actors or their presence in the same place at the same time, e.g. sitting next to each other, attending the same party, visiting a person’s homemovement: physical (migration from place-to-place), social (movement between occupations or statuses)formal roles: e.g. dictated by power and authority in a management settingkinship: marriage, descent
38 Actor Attributes People can be queried about different features, like agegenderracesocioeconomic statusplace of residencegrade in school, etc.
39 Two Sets of Actorsfocus on two sets of actors, or one set of actors and one set of eventsRelations measure ties between the actors in one set and actors in a second setDescribed as dyadic two-mode networks, because actors from the first set are different from the actors of the second setWasserman/Faust 2008:39
41 What is a Network Society? A new techno-economic system (society) where the key social structures and activities are organized around electronically processes information networksSocial Structures:involve the organized arrangements of humans in relations of production, consumption and reproduction,experiences and power expressed in meaningful communication coded by cultureNetworks:a set of interconnected nodes, with no centrenetworks have been very old forms of social organizationIt is about social networks which process and manage information and are using micro-electronic based technologies
42 What is a Network Society? Social integration/impactThe demise of Mass audiencesTwo-way communication and interactivityThe death of time and distancePersonalized mediaGlobalization and Cultural standardizationTransformations in Politics and democracy (see virtual political parties, e-voting, e-referenda, e-advocacy, e-news etc)Transformation of work and employment
43 Castells calls three main trends for the rise of a network society - The process of transformation to a network society started in the 1970s through the interaction of three independent trends:the invention of microelectronics and the IT revolutionthe crisis of industrialism in both capitalist and statist societies,the profound cultural challenge mounted by the rise of social movements in the late 1960s
44 Castells, M. (1991), The Informational City Castells, M. (1991), The Informational City. Information Technologies, Economic Restructuring, and the Urban-Regional Process, Oxford and Cambridge, Basil Blackwellnetwork society is a social order embodying a logic like ‘space of flows’space of flows is the material organization of time-sharing social practices that work through flowsflows are purposeful, repetitive, programmable sequences of exchange and interaction between physically disjointed positions held by social actors in the economic, political, and symbolic structures of societypresence and absence are critical sources of domination and change in our society
45 Castells, M. (1991), The Informational City New information technologies are integrating the world in global networks of instrumentalityIn the new, informational mode of development the source of productivity lies in the technology of knowledge generation, information processing, and symbol communicationthe action of knowledge is the main source of productivity
46 On social capitalscholars do not agree whether it refers to ‘resources’ or networks or a combination of social structure and networks and ideas and values associated with themFollowing Foley and Edwards (2001) who reviewed the literature found that the term is mainly used to refer to associational life or social networks and not to social norms as suchFour important sociologists, however, focus on actor-centered and network-related social capital as a valuable resource: Pierre Bourdieu, James Coleman, Robert Putnam and Francis Fukuyama
47 Pierre Bourdieuconsiders social capital of an actor as an exploitation of a permanent net of more or less institutionalized relations of mutual knowledge and recognitionconsiders social capital as a resource among other capital forms (economic capital, cultural capital, symbolic capital)Social capital is based upon membership to a groupThe larger social net of personal relationswhich he can take reference tohigher profit chances in the reproduction of his economic and cultural capital
48 James ColemanSocial capital is a variety of different entities, with two elements in common: “They all consist of some aspect of social structures, and they facilitate certain actions of actors - whether persons or corporate actors - within the structure.”unlike other forms of capital, social capital inheres in the structure of relations between actors and among actorsColeman 1988: 98
49 Network Analysis and Social Capital Social capital can be understood under a network theoretical approach as an aspect of the social structure which enlarges or restricts individual or corporative actionsin opposite to economic and human capital, social capital is not only restricted to the single actor but to his relations to other actors and their positions within the networkother actors who are not directly linked with the focussed actor are able to influence the situation indirectly
50 Network Analysis and Social Capital - Its hinge function between actors (individuals, collectivs, corporates) Körperschaften) and social structure offers the focus on following fields of interest:(1) Question about social capital of a single actor within a network and ist possibilities of strategial influence(2) Question about how different actors can be compared with regard to their positions within the network(3) Question which influence does social capital have onto the network as well as onto the whole society
51 network-theoretical considerations I Granovetter’s (1977) linkage of network morphology with action, by considering strong and weak network tiesAmong strong relations there is the tendency of cluster formation, whereas a linkage between different clusters can only occur by weak ties that form bridges between theseThe ‘Strength of Weak Ties’ (the title of this article) is therefore their ability to open up closed networksWeak ties: more of them with unconnected others, better for finding jobsStrong ties: less of them with related others, better for trustRecent approaches that apply Granovetter’s distinction to the notion of social capital, distinguish ‘bonding capital’ (between people) and ‘bridging capital’ (between groups).
52 Social Network Theories Strong tiesTrust that exchange partners will not act in self-interest at expense of othersCreates ideal conditions for:Knowledge diffusionCollaborative problem solvingClimate of informal governanceOptimization of member contributions(Levin and Cross, 2004)
53 Social Network Theories Strength of weak ties Networks based on weak ties (distant and infrequent relationships) are more efficient at sharing knowledge as they provide access to novel information from otherwise disconnected partiesLess “dense” networks:Reduce redundancy of information/resourcesIncrease diversity of resources(Granovetter , 1982)
54 Francis Fukuyamaconsiders social capital as an important factor for welfare and competitiveness of a nationsocial capital is a given set of informal norms and values, which all members of a group share, and which facilitate cooperation between the group membersWhen these assume that others will behave in a trustful and reliable way, they will trust each other (Fukuyama 1992: 32)the ability and capacity to communicate in an uncomplicated way and to cooperate is a ‘spontaneous solidarity’, which constitutes an important part of social capitalIt plays an important role in the creation and maintenance of civil society, because spontaneous sociability enables people, who do not know each other, to congregate and cooperate with each other
55 Alena Ledeneva : The Concept of Blat Alena Ledeneva : The Concept of Blat. The Network Economy in Post-Soviet Russiadefines blat “as an exchange of ‘favours of access’ to public resources in conditions of shortages and a state system of privileges” (Ledeneva, 1998:37)Through blat networks public resources were redirected to private uses and to the needs of personal consumptionThese relations were often disguised by the rhetoric of friendship, such as ‘helping out’ a friend or an acquaintance
56 Alena Ledeneva : The Concept of Blat Alena Ledeneva : The Concept of Blat. The Network Economy in Post-Soviet Russiasees blat networks as both vital to the Soviet social order and subversive of itThey were needed in most aspects of daily life in the Soviet Union such as obtaining foodstuffs, train tickets, medical services, study places at university or specialized schools, jobs, cars, and apartmentsMost of the restrictions and harshness of everyday life could in fact be avoided by blatdistinguishes blat from apparently similar phenomena, e.g. clientelism and other corrupt practices, by being less morally doubtful and therefore more pervasiveblat was based on personal relations implying continuity of the relationship and was often disguised as friendly helpblat was only conceivable in the context of socialist shortage economy and the state-governed system of distribution.
57 But what happened to these networks with the collapse of communism? Alena Ledeneva : The Concept of Blat. The Network Economy in Post-Soviet Russiathe role of networks is clearly present in the studies of the “second”, “shadow” or ”informal” economy of the Soviet Union, post-Soviet Russia, SU-successor states and Eastern EuropeBut what happened to these networks with the collapse of communism?Are they still viable in post-socialist society?
58 Alena Ledeneva : The Concept of Blat Alena Ledeneva : The Concept of Blat. The Network Economy in Post-Soviet RussiaLedeneva argues that the network economy is inherited from the Russian/Soviet past and carries features inhibiting democratic developmentThe relationship between formal institutions and informal networks is more complicated than thatargument: the fundamental principle of the network economy, however, has not change, but following political, economic and social changes, informal networks started modifying and filling in available and newly created loopholes.
59 V. meeting: Introduction in the computer programme „UCINET“ "Introduction in Social Network Analysis. Theoretical Approaches and Empirical Analysis with computer-assisted programmes."V. meeting:Introduction in the computer programme „UCINET“
60 UCINET--Introduction UCINET—UCINET is produced by Analytic Technologies. It offers a very user-friendly, reasonably priced software system for network analysis.Throughout this discussion, we’ll use the example of the cosponsorship network of the 58 legislators in the lower house of the Arizona legislature, 2001.
61 Starting UCINETWhen you first open UCINET, set the default directory to a directory of your choice, by typing in the directory name (into the space at the bottom edge of the UCINET window). Note that the original default directory is just the c:\ drive.Note that UCINET produces many types of files—and deleting any (before you are entirely done with your analysis) may make it difficult to use some of the others.
62 QAP ProcedureUCINET also allows the possibility of a regression analysis, using a QAP procedure.The QAP Procedure will be the focus of our next discussion.
63 UCINET--Introduction offers a very user-friendly, reasonably priced software system for network analysisThroughout this discussion, we’ll use the example of the cosponsorship network of the 58 legislators in the lower house of the Arizona legislature, 2001.
64 Starting UCINETWhen you first open UCINET, set the default directory to a directory of your choice, by typing in the directory name (into the space at the bottom edge of the UCINET window). Note that the original default directory is just the c:\ drive.Note that UCINET produces many types of files—and deleting any (before you are entirely done with your analysis) may make it difficult to use some of the others.
65 How to Read Data into UCINET There are several ways to read network data into UCINET. I’ll review two basic methodsusing matrices, and using dl language.UCINET can read in a matrix data—either saved in a text file, or saved in excel.So, in the case of the Arizona cosponsorship data that we will use as an example, there are 58 legislators – and therefore 58 X 58 = 3,364 dyads.
71 various questions can be answered Which player initiated the most passes (Jazic)?Who was on the receiving end of the most passes (Jazic)?Who controlled Rapid’s play (Jazic, Hoffman)?Which players were involved in the most combination pass plays (Jazic, Hofmann, Feldhofer, Martinez, Carics)?Who played together with whom andwho didn’t (not a single pass from Ivanschitzto Wagner!)?Which combinations of players made upthe backbone of the team(e.g. the Feldhofer-Carics-Pashazadeh triad)?Which players had a similar role(Ivanschitz / Martinez)?71
73 Which player initiated the most passes? Who was on the receiving end of the most passes?Who has controlled England’s play?Which players did not play together?Which players had a similar role?
74 SNA – linkage between Visualization and Data Graph theory is universally applicable in modeling social relationshipsData on social relationships are transformed into graphs and evaluated on different analytical levelslevels base on the individual agent, dyadic or triadic level, cluster level, level of the entire networkc.f. Katzmeier (2007): Social Network Analysis. The Science of Measuring, Visualizing and SimulatingData on Social Relationships, Working Paper Series, Vienna
75 Typical Social Relationships for Network Analytical Consideration: c.f. Katzmeier (2007): Social Network Analysis. The Science of Measuring, Visualizing and SimulatingData on Social Relationships, Working Paper Series, Vienna
76 Software for Social Network Analysis Huisman, van Duijn (2003): Software for Social Network Analysis, University of Groningen, Working Paper Series, p.3
77 "Introduction in Social Network Analysis "Introduction in Social Network Analysis. Theoretical Approaches and Empirical Analysis with computer-assisted programmes."IV. meeting:Short overview about computer programme „Pajek“Introduction in the computer programme „VISONE“
80 What is PajekPajek is a program, for Windows, for analysis of large networks.Authors:Andrej Mrvar, Faculty of Social Sciences, University of Ljubljana.Vladimir Batagelj, Faculty of Applied Mathematics, University of Ljubljana.Pajek started to develop in November 1996.Pajek is freely available, for noncommercial use, at its homepage
81 PajekPajek (Version 0.94; Batagelj and Mrvar, 2003a) is a network analysis and visualization program, specially designed to handle large data setsmain goals in the design of Pajek are:1) to facilitate the reduction of a large network into several smaller networks that can be treated further using more sophisticated methods2) to provide the user with powerful visualization tools, and3) to implement a selection of efficient network algorithms (Batagelj and Mrvar, 1998)
82 With Pajek we can findclusters (components, neighborhoods of ‘important vertices, cores, etc.) in a networkextract vertices that belong to the same clusters and show them separately, possibly with the parts of the context (detailed local view)shrink vertices in clusters and show relations among clusters (global view)
84 Pajek Pajek uses six different data structures: networks (nodes and arcs/edges),partitions (classifications of nodes, where each node is assigned exclusively to one class),permutations (reordering of nodes)clusters (subsets of nodes),hierarchies (hierarchically ordered clusters and nodes), andvectors (properties of nodes)
94 Visonea tool that facilitates the visual exploration of social networksan attempt to integrate analysis and visualization of social networksorigins of Visone lie in an interdisciplinary cooperation with researchers from political science whichresulted in innovative uses of graph drawing methods for social network visualization, and prototypical implementations thereofIn a nutshell, Visone is atool for interactive analysis and visualization of networks, in whichoriginality is preferred over comprehensiveness, and thatcaters especially to social scientists.94
95 ModelA social network consists of nodes (often referred to as actors), i.e. entities such as persons, organizationssimply objects that are linked by binary relations such as social relations, dependencies, or exchangeBoth nodes and links may have additional attributesRelations constituting a social network may be directed, undirected, or mixedAttributes can be of any type, and numerical link attributes may strengthen or weaken the tie between two nodes95
96 Analysispurpose of social network analysis is to identify important actors, crucial links, roles, dense groups, and so on, in order to answer substantive questions about structureanalysis methods available in visone are divided into four main categories according to the level or subject of interest: vertex, dyad, group, and network levelavailable analysis methods include actor-level centrality indices, e.g. closeness, betweenness, and pagerank, cohesive subgroups like cliques, k-cliques, and k-clans, centrality and connectednessThese levels break further down into measures of the same objective, e. g., connectedness or cohesivenessanalysis methods are accessible using the analysis tab in the control area96
97 AnalysisThe purpose of social network analysis is to identify important actors, crucial links, subgroups, roles, network characteristics, and so on, to answer substantive questions about structuresThere are three main levels of interest: the element, group, and network levelOn the element level: one is interested in properties (both absolute and relative) of single actors, links, or incidences, e.g. structural ranking of network itemsOn the group level: one is interested in classifying the elements of a network and properties of sub-networks, e.g. actor equivalence classes and cluster identificationOn the network level: one is interested in properties of the overall network such as connectivity or balance97
98 Confirmation also called reciprocity Unconfirmed edges emerge for example when two actors have divergent perceptions of the existence or specificity of their relation or when one of them simply liesSuch unconfirmed connections exhibit an additional form of direction induced by the actor who test ties for ita directed edge is called sender confirmed if it is confirmed by its tail and receiver confirmed if it is confirmed by the head98
99 Characteristics of Input Data DirectionEdge WeightsMulti-EdgesLoops99
100 DirectionTypically, a formulation of an algorithm allowing directed edges is more general than one for undirected edges since for almost all purposeseach undirected edge fu; vgis replaced equivalently by two symmetric, contrariously directed edges (u; v) and (v; u)one. In particular, two symmetric, contrariously directed edges (u; v) and (v; u) are replaced by two undirected edges fu; vg which may be unintentional100
101 Are depending on the context: strength (larger is better) or Edge WeightsAre depending on the context:strength (larger is better) orlength (smaller is better)for each method, it is clearly labeled if a weight is considered as strength or as lengthFor some methods, even two weights of dierent meaning can be speciedHowever, it is the user's responsibility to select a reasonable attribute as weight101
102 Weights and Attributes one is not only interested in the existence of edges but in a quantication of the interconnectionsthis may be the frequency of meetings, the helpfulness of advice, or the costs of exchange
104 The main use cases of attributes are: store user data, e. g., weights and semantical element information,specify input parameters of analyses methods, typically as edge weights,store the result of analyses methods, e. g., centrality indices, a partitioning, orclique membership, andspecify input parameters of visualizations, e. g., the index or the partitioningto depict in a drawing.
105 Visualizationthere are two obvious criteria for the quality of social network visualizations:the information manifest in the network represented accurately?Is this information conveyed efficiently?the following three aspects should be carefully thought through when creating network visualizations:the substantive aspect the viewer is interested in,the design (i.e. the mapping of data to graphical variables), andthe algorithm employed to realize the design (artifacts, effciency, etc.)105
113 Exercise 5 a b c d e a b c d e Build a socio-matrix a b c e d a b c e From pictures to matricesabcedabcedUndirected, binaryDirected, binaryabcdeabcde
114 Exercise 5 a b c d e 1 a b c d e 1 Build a socio-matrix a b c e d a b From pictures to matricesabcedabcedUndirected, binaryDirected, binaryabcde1abcde1
115 Social Network Properties Centrality and Power
116 Degree Number of links that a node has It corresponds to the local centrality in social network analysisIt measures how important is a node with respect to its nearest neighbors
117 Fundamental IdeasAB, AE, and BE have path length of 1 (1 line connects each pair of points)A and C are connected through B and have a path length of 2 (2 lines)there are no isolated pointsevery point can reach every other point within 2 stepsA CBD E
118 Fundamental Ideas AD has a path lenth of 1 the walk ABCAD is not a path (passes through A twice!)ABCD has a path length of 3A and D are connected by 3 pathsAD – length 1ACD – length 2ABCD – length 3the distance between A and D is equal to the shortest pathA BD C
119 Fundamental Ideasdirected graphs are similar except for the possible assymetry of the relationshipdegree has two separate components:indegree: total numbers of alters related to ego; A=1, B=2, C=1outdegree: total numbers of points ego relates to; A=1 , B=1 , C=2paths: CAB is a path, CBA is not a path!BAC
120 Graph Density describes the general level of contectedness in a graph graph is complete if all points are adjacent to each otherthe more points that are connected, the greater the densitythere are two components for densityinclusiveness: number of points that are included in the graph because they are connectedtotal degree: sum of degree of all the points
121 Graph DensityDensity is defined as the total number of observed lines in a graph divided by the total number of possible lines in the same graph Density ranges from 0 to 1 L 2 L D = = g * (g-1) g * (g-1) 2 L = number of lines; g = number of points