Social Networks Analysis Week 2

sna measurements Relational Data From Social Data to Relational Data Nodes & Ties Dyad Triad Subgroup Group Degree Centrality and Power Density Path Length & Neighborhoods Small World Clustering Coefficient Structural Hole Clique

Node/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 system Does not imply that they have volition or the ability to “act”

Size Number of Nodes

Ties/Links Different types of ties: family, friend, personal / professional, ego-perceived / alter-perceived / mutual Directed (Flickr) / Undirected (Facebook) Strong & Weak ties Amount of time, emotional intensity, intimacy and reciprocal services

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)

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 is Transitive : if actor i “likes” actor j, and actor j in turn “likes” actor k, then actor i will also “like” actor k Balanced: 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

Subgroup Subgroup of actors is defined “as any subset of actors, and all ties among them” (Wasserman/Faust 2008:19)

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)

Degree Number of links that a node has It corresponds to the local centrality in social network analysis It measures how important is a node with respect to its nearest neighbors Directed Graph Indegree & Outdegree

What is the size of the graph What is the In-Degree & Out-Degree of Node 5 ? What is the In-Degree & Out-Degree of Node 4 with weight ?

Path Length AB, 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 points every point can reach every other point within 2 steps

Path AD has a path length of 1 the walk ABCAD is not a path (passes through A twice!) ABCD has a path length of 3 A and D are connected by 3 paths AD – length 1 ACD – length 2 ABCD – length 3 the distance between A and D is equal to the shortest path

Path directed graphs are similar except for the possible asymmetry of the relationship degree has two separate components: indegree: total numbers of alters related to ego; A=1, B=2, C=1 outdegree: total numbers of points ego relates to; A=1 , B=1 , C=2 paths: CAB is a path, CBA is not a path!

What is the path length from node 1 to node 9 Shortest path

Centrality & Power

Network & Power Who has more power

Centrality Degree, Betweenness, Closeness, Eigenvalue

Centrality in Social Networks : Degree The most intuitive notion of centrality focuses on degree: The actor with the most ties is the most important:

Centrality in Social Networks : Degree

The closeness of node 4 in this graph The betweeness of node 5 in this graph

Graph Density describes the general level of contectedness in a graph graph is complete if all points are adjacent to each other the more points that are connected, the greater the density there are two components for density inclusiveness: number of points that are included in the graph because they are connected total degree: sum of degree of all the points

Graph Density

Graph Density Example

The density of this graph?

Clustering Friends of friends are likely to be friends Clustering coefficient, C (0 <= C<= 1) Density of triangles in the network Density of links that exist between one’s friends

Cluster Coefficient

The clustering coefficient of node 1, 2, 3, 4, 5, 6

Structural Hole

Clique Measurement Clique Complete subgraph Maximum clique {1,2,5} Maximal cliques {2,3}, {3,4}, {4,5},{4,6} K-clique Clique of size k

Please find all the 3-cliques in this graph