Basic Concepts

Edges have no orientation (order not important)

Adjacency Matrix is symmetric

Degree & Total number of Edges:

Each edge has an origin and a destination

In degree ki in

Out degree ki out

ki = sum of ki in + sum of ki out

average in-degree & average out degree is equal

Asymmetric adjacency matrix

Undirected/Directed graphs where edges can occure more than once

if two vertices are joined by an edge, they are adjacent = neighbors

direction from the ehdes run from second to first index

degree k can be obtained from the adjacency matrix

each edge has an additional numerical value

graph where each edge is between a pair of vertices

Number of edges of a complete undirected graph with N vertices:

Number od edges of a complete directed graph with N vertices:

For undirected graphs:

for directed:

path: sequence of nodes where each pair od nodes is connected by an edge

distance: the distance between to vertices in a graph is defined as the length of the shortest path between the,

Average distance: mean of fionite dinstances between all pairs of vertices

diameter: longest distance (longest shortest path) between any pair of vertoces which have a path

A path with at least three edges is a cycle if the first and last edge are the same but otherwise all vertices are distinct

when each edge is traversed once in a path