D IPARTIMENTO DI I NGEGNERIA INFORMATICA AUTOMATICA E GESTIONALE A NTONIO R UBERTI Master of Science in Engineering in Computer Science (MSE-CS) (MSE-CS) Seminars in Software and Services for the Information Society Umberto Nanni Social Networks – Basic concepts Umberto Nanni Seminars of Software and Services for the Information Society 1
An old paper 1955 No one supposes that there is any connexion between horse-kicks suffered by soldiers in the German army and blood cells on a microscope slide other than that the same urn scheme provides a satisfactory abstract model of both phenomena. Umberto Nanni Seminars of Software and Services for the Information Society 2
A quote “If we make a chart of social interactions, of who talks to whom, the clusters of dense interaction in the chart will identify a rather well-defined hierarchic structure. will identify a rather well-defined hierarchic structure. The groupings in this structure may be defined operationally by some measure of frequency of interaction in this sociometric matrix.” The Sciences of the Artificial , Cambridge, MA, MIT Press, 1969. Herbert Alexander Simon [1916 – 2001] • 1975: Turing award • 1978: Nobel award (Economy) Umberto Nanni Seminars of Software and Services for the Information Society 3
Power Law (Pareto’s law, Zipf’s law) population of cities • y = c x −α + ε(...) magnitude of earthquakes • y = c x + ε(...) craters of the moon • sunspots sunspots • • file size • “size" of the wars • frequency of use of the words • frequency of proper names • number of articles written by scientists • number of citations of articles • per capita income per capita income • • number of species in taxonomies • accesses to pages on the web • sales of: books, music pieces, many products sold on the web • ... • Umberto Nanni Seminars of Software and Services for the Information Society 4
Some examples number of web sites number of web sites number of users number of users A day of web accesses by AOL users Umberto Nanni Seminars of Software and Services for the Information Society 5
Some examples percentage population of cities Umberto Nanni Seminars of Software and Services for the Information Society 6
Some examples Umberto Nanni Seminars of Software and Services for the Information Society 7
Some examples Umberto Nanni Seminars of Software and Services for the Information Society 8
Parameters in the power law Umberto Nanni Seminars of Software and Services for the Information Society 9
Social Network NODES: set of subjects ARCS: binary relation between instances that are part of a given set The relation giving rise to arcs: - may NOT be symmetrical - may NOT be symmetrical - can be derived from relationships with other entities Umberto Nanni Seminars of Software and Services for the Information Society 10
Social networks • membership of a social network can be: – conscious, with an explicit declaration of links – unconscious, placement into groups depends on a relatively homogeneous behavior Umberto Nanni Seminars of Software and Services for the Information Society 11
Social Networks – more examples • World Wide Web • Internet Internet • citations between scientific papers • citations between authors • direct knowledge between individuals • business relationships between companies • sending e-mail • sending e-mail • (biology) involvement of proteins in a process • telephone communications • ... Umberto Nanni Seminars of Software and Services for the Information Society 12
Personal acquaintedness Umberto Nanni Seminars of Software and Services for the Information Society 13
Sociogram Graphical representation of a social graph with a metaphor that provides quantitative evidence of metaphor that provides quantitative evidence of the weight of the arcs, together with the verse. Jacob L. Moreno, 1934 (!) Umberto Nanni Seminars of Software and Services for the Information Society 14
Historical Experiments on a Social Network 1967: Milgram Experiment • letters sent to specific recipient • it can be sent only to a recipient personally • it can be sent only to a recipient personally known • 5% success; distance-average = 6 1969 Travers-Milgram Experiment • compared to the previous more information about the recipient • 29% success; distance-average = 5.2 Small World Phenomenon Umberto Nanni Seminars of Software and Services for the Information Society 15
Communities in social graphs Bipartite components: • HUB: nodes with many leaving arcs • AUTHORITIES: nodes with many entering arcs • AUTHORITIES: nodes with many entering arcs componente bipartita completa authority hub Social Networking Potential (SNP) • alpha subject Umberto Nanni Seminars of Software and Services for the Information Society 16
Social Networks – some metrics and properties • in/out degree g in , g out : number of entering/leaving arcs • diameter d : maximum distance between a pair of nodes → Small World Phenomenon • neighborhood N(h) : number of nodes within distance h Umberto Nanni Seminars of Software and Services for the Information Society 17
More metrics on Social Networks • Betweenness: Degree an individual lies between other individuals in the network; the extent to which a node is directly connected only to those other nodes that are not directly connected to each other; an intermediary; liaisons; bridges. • Closeness: The degree an individual is near all other individuals in a network (directly or indirectly). It reflects the ability to access information through the "grapevine" of network indirectly). It reflects the ability to access information through the "grapevine" of network members. Thus, closeness is the inverse of the sum of the shortest distances between each individual and every other person in the network. • (Degree) centrality: The count of the number of ties to other actors in the network. See also degree (graph theory). • Flow betweenness centrality: The degree that a node contributes to sum of maximum flow between all pairs of nodes (not that node). • Eigenvector centrality: a measure of the importance of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections to nodes having a high score contribute more to the score of the node in question. nodes having a high score contribute more to the score of the node in question. • Centralization: The difference between the n of links for each node divided by maximum possible sum of differences. A centralized network will have many of its links dispersed around one or a few nodes, while a decentralized network is one in which there is little variation between the no. of links each node possesses • Clustering coefficient: A measure of the likelihood that two associates of a node are associates themselves. A higher clustering coefficient indicates a greater 'cliquishness'. Umberto Nanni Seminars of Software and Services for the Information Society 18
More metrics on Social Networks • Cohesion: The degree to which actors are connected directly to each other by cohesive bonds. Groups are identified as ‘cliques’ if every actor is directly tied to every other actor, ‘social circles’ if there is less stringency of direct contact, which is imprecise, or as structurally cohesive blocks if precision is wanted • (Individual-level) density: the degree a respondent's ties know one another/ proportion • (Individual-level) density: the degree a respondent's ties know one another/ proportion of ties among an individual's nominees. Network or global-level density is the proportion of ties in a network relative to the total number possible (sparse versus dense networks) • Path Length: The distances between pairs of nodes in the network. Average path-length is the average of these distances between all pairs of nodes • Radiality: Degree an individual’s network reaches out into the network and provides novel information and influence • Reach: The degree any member of a network can reach other members of the nework • Structural cohesion: The minimum number of members who, if removed from a group, • Structural cohesion: The minimum number of members who, if removed from a group, would disconnect the group • Structural equivalence: Refers to the extent to which actors have a common set of linkages to other actors in the system. The actors don’t need to have any ties to each other to be structurally equivalent • Structural hole: Static holes that can be strategically filled by connecting one or more links to link together other points. Linked to ideas of social capital: if you link to two people who are not linked you can control their communication Umberto Nanni Seminars of Software and Services for the Information Society 19
Some Social Networks • G int Internet Graph – degrees according Power Law • G web Web Graph – degrees according Power Law – diameter aboput 20 (Small World Phenomenon) • G mail e-mail Graph – degrees according Power Law – degrees according Power Law • Facebook Graph • ... Umberto Nanni Seminars of Software and Services for the Information Society 20
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