Generally, social network is represented as an

undirected graph and it reveals much useful information regarding vertices (users), such as vertex degree (number of connections), neighborhood structure, mutual relations, etc.

The network is modeled by an

undirected graph and each SRLG is modeled by a color assigned to some of the edges of this graph.

Firstly, converting tweets and users to nodes we created a connected

undirected graph.

Let a network be modeled by a simple

undirected graph G = (V, E) with k nodes and m edges.

Notice that the above model of

undirected graph, which is best suited for routing in social systems.

It can be explained as bellow: (1) network G is a simple

undirected graph with n nodes; (2) tree map D is a binary tree, and it has n leaves corresponding to the n nodes of G; it also has n-1 internal nodes corresponding to the node pairs formed in D; (3) Node i and Node j are two nodes of network G, and the probability that these two nodes will be linked with the edge is given as pij; r is the nearest common ancestor of Node i and j in tree map D.

The Laplacian matrix of a weighted,

undirected graph is defined as L = D - A, where D is the diagonal matrix containing the sum of incident edge weights and A is the weighted adjacency matrix.

A digraph is connected (or weakly connected) if its underlying

undirected graph is connected.

We consider several problems asking whether an

undirected graph G admits orientations satisfying some connectivity and distance properties.

For an

undirected graph, if there exist paths from every agent to every other agent, then the graph is connected.

In an

undirected graph, the elements are not ordered pairs, but are simply sets of vertices.

The total number of links to be in the network is derived from the LD value for

undirected graph.