Descriptive Network Analysis

• All graphs are represented with as an ordered pair of vertices and edges G=(V,E)
• For describing a network graph, we set n=# vertices and m=# edges
• An edge is an ordered pair of vertices, e34 connects nodes 3 and 4
• Adjacency matrix 


  An NxN matrix, where N is the number of nodes, a 1 in position i,j represents a connection between nodes i and j

  
• Twitter could be represented as a directed graph, where A follow B
• Facebook could be represented as a non directed where A and B nodes are "friends"
• Adjacency matrices for non directed graphs are symmetric matrices
• Adjacency matrices can also have values other than 0/1, higher numbers could represent edge strength
• In a directed graph, a 1 in row i and column j means that the edge is from node i to node j
• Incidents are the number of edges on a node
• Neighbourhood of a node V is th set of all adjacent nodes to V, e.g. N(V)={1,2,5,7}
• Degree of a vertex is the sum of its incident edges
• Average node degree is a common way of describing a node's connections
• (insert AVG edge formula)