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
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