Prominence: Reflects its greater visibility to the other network actors
Prestige
Centrality
Central actors
Peripheral actor
Centrality Measures
Degree: Nodes with higher value are more central in undirected graphs
Types
Indegree: Nodes with higher value are more central in directed graphs
Outdegree: Nodes with higher value are more prestigious in directed graphs
Measures
Actor level
Group degree: Quantifies the dispersion or variation among individual centralities
Freeman Group Degree Centrality
Variance of the degrees
Mean Degree
Standardized Average Degree = Mean Degree/(g-1) = Density
Closeness
Fairness/Peripherality: Total distance that actor i is from all other actors
Actor Closeness = 1/Fairness
Group Closeness
Freeman's general group closeness index
Improved actor-level centrality closeness index
Betweenness
Group Betweenness
Freeman's group betweenness centralization index
Eigen Vector Centrality (Eigencentrality) Measure: Measure of the influence of a node in a network
Steps
Construct matrix A, representing connection between nodes based on given graph
Solve for |A - λI| = 0, to get non-zero eigen values
Solve corresponding to largest (Principal) eigen value, (A - λI)V = 0
V is the eigen vector, Assume one value to be "t" in general solution
Clustering Coefficient: Measure of the degree to which nodes in a graph tend to cluster together
Local version: Gives an indication of the embeddedness of single nodes
Local Clustering Coefficient = Number of links between vertices within its neighborhood/Number of links that could possibly exist between them
Clustering coefficient = Number of connections in the neighborhood of a node/Number of connections if the neighborhood was fully connected
Global version: Gives an overall indication of the clustering in the network
Clustering coefficient = Number of triangles connected to node i/Number of triples centered around node i = Number of closed triplets/Number of connected triplets of vertices = (3 × Number of triangles)/Number of connected triplets of vertices
Connected Triplet: A connected subgraph consisting of three vertices and two edges
Transitivity of Graph = 3 × Number of triangles in the network/Number of connected triples of
nodes in the network
Reciprocity of Graph
In Directed network is the fraction of edges that belong to a loop of length two
EGO Network
Network consisting of a single node (ego) together with the nodes it is connected to (alters) and all the links among those alters
Diameter = 2
Size = Number of contacts an EGO has
Redundancy = Number of EGO alter/Size of EGO
Effective Size = Number of EGO alters – Sum of Redundancy of EGO alters
Efficiency = Effective size/Actual size
Weak components: Largest number of actors who are connected, disregarding the direction of the ties
Structural Hole: Gap between two individuals who have complementary sources to information
A hole between two contacts, provide network benefits to the third party