1. NOTATION FOR SOCIAL NETWORK DATA Three network schemas to represent a wide range of network data Graph theoretic Sociometric Algebraic A graph consists of nodes connected by lines. The symbol N is used to indicate a set of actors/nodes in a graph, denoted as {N 1, N 2,…N n }

2. A set Suppose we have a collection of 6 actors N = {N 1 = Allison; N 2 = Drew; N 3 = Eliot; N 4 = Keith; N 5 = Ross; N 6 = Sarah} A single relation: we define a relation and see how each actor is related to other actors on this relation. To start, we assume the relation to be dichotomous and directional.

3. Ordered pair Dichotomous relations mean either the relation among actors/nodes present or absent in a graph Directional ties mean relationship from actor A to B is distinctive from the relationship from actor B to A. Ordered pair denotes a pair of actors/nodes related from actor I to actor J on a relationship. How many ordered pair can be present in a directional graph with g nodes/actors?

4. A Graph A graph consists of a number of nodes and a number of lines connecting those nodes G (N{n 1, n 2, … n n }, L{l 1, l 2, … l n }) Valued graphs have one more factor of values attached to each line G (N{n 1, n 2, … n n }, L{l 1, l 2, … l n }, W{w 1, w 2, … w n }) Some graphs have directions attached to each line, which are called directed graphs

5. Classification of Graphs Four types of graphs Non-directedDirected BinaryBinary, non- directional graphs Binary Directional Graphs ValuedValued, non- directional graphs Valued, directional graphs

6. Multiple Relations Sometimes, graphs can encompass more than one relation among their actors. Mathematically, we denote those graphs as G (N{n 1, n 2, … n n }, L{l 1, l 2, … l n }, R (r 1, r 2, …r n ))

7. Sociometric Notation Sociometric notation is another way to describe a matrix network dataset in addition to graph representation X ij = the value of the tie from n i to n j To capture multiple relationship among actors X ijr = the value of the tie from n i to n j on relation X R.