A signed graph is a simple graph where each edge receives a sign positive or negative. Such graphs are mainly used in social sciences where individuals represent vertices friendly relation between them as a positive edge and enmity as a negative edge. In signed graphs, we define these relationships (edges) as of friendship ("+" edge) or hostility ("-" edge). A 2-path product signed graph [Formu...

The increasingly booming online social networks promote the development of online health forum. People tend to solve kinds of health issues through the Internet. However, it is still unclear what the main characteristics of friendship networks are and how the users’ attribution affect the friendship ties establishment in the online health forum. This study uses the Exponential Random Graph Mode...

Abstract Many empirical studies have shown that in social, citation, collaboration, and other types of networks real world, the degree almost every node is less than average its neighbors. This imbalance well known sociology as friendship paradox states your friends are more popular you on average. If we introduce a value equal to ratio neighbors for certain this (which called ‘friendship index...

Previous research suggests that social anxiety disorder (SAD) has a specific relationship with impairment in friendship quality; however, potential moderators of this relationship have not been tested. The current study examines whether the specific effect of SAD on friendship quality is stable or varies across gender and ethnicity in a large epidemiological dataset. Results indicate that the u...

Unilateral friendships provide a powerful mechanism to study friendship formation, because these friendships contain interest in friendship, but have not yet become full, reciprocated friendship. This longitudinal study investigated whether the conversations of unilateral dyads identified in the fall were predictive of that dyad’s relationship status in the winter. I hypothesized that the conve...

Let G∗ = (V, E) be a simple graph and A any nonempty set of parameters. subset R A×V an arbitrary relation from to V. mapping ᵖ(V) written as F:A → can defined F(x) { y ∈ V/xRy} ᵖ(E) K:A K(x) {uv E/{u, v} ⊆ F(x)}. The pair (F, A) is soft over V the (K, E. Obviously (F(a), K(a)) subgraph for all A. 4-tuple G ( G∗, F, K, called G. In this paper we discuss different graphs such Complete graph, Sta...

A distance magic labeling of a graph G = (V, E) of order n is a bijection l : V → {1, 2, . . . , n} with the property that there is a positive integer k (called magic constant) such that w(x) = k for every x ∈ V . If a graph G admits a distance magic labeling, then we say that G is a distance magic graph. In the case of non-regular graph G, the problem of determining whether there is a distance...

Why do your friends have more friends than you do? The question may sound offensive. We don’t even know you. How can we assume than you have fewer friends than your friends have on average? Because most people do. This so-called friendship paradox has first been described and studied in [1]. It does seem counterintuitive: If we are talking about the average number of friends of average friends ...