For any simple graph H, let σ(H,n) be the minimum m so that for any realizable degree sequence π = (d1, d2, . . . , dn) with sum of degrees at least m, there exists an n-vertex graph G witnessing π that contains H as a weak subgraph. Let Fk denote the friendship graph on 2k+1 vertices, that is, the graph of k triangles intersecting in a single vertex. In this paper, for n sufficiently large, σ(...

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...

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...

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...

Online Social Networking (OSN) services have become among the most popular services on Internet and their growth has led to creation of lots of different applications and protocols. Most of these applications and protocols rely on findings of previous studies which were concentrated on analyzing and modeling of the structure of inferred friendship graph of social networks. However, serious ques...

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 ...