Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...

The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment...

This study examined differences in kin and nonkin networks among African Americans, Caribbean Blacks (Black Caribbeans), and nonHispanic Whites. Data are taken from the National Survey of American Life, a nationally representative study of African Americans, Black Caribbeans, and non-Hispanic Whites. Selected measures of informal support from family, friendship, fictive kin, and congregation/ c...

Although it is clear that people with social phobia have interpersonal impairment, evidence that social phobia (as opposed to other mental disorders) affects friendship in particular is lacking. Two large epidemiological datasets were used to test whether diagnosis of social phobia is related to perceived friendship quality above and beyond perceived family relationship quality, diagnosis of ot...

The friendship paradox is revisited by considering both local and global averages of friends. How the economics of attention affects the recruitment of friends is examined. Statistical implications of varying individual attentions are investigated and it is argued that this is one reason why the mean of friends is higher than the median in social networks. The distribution of friends skews to t...

One of the principal themes of the Conference on Actualizing Human Potential has been that of hospitality. While hospitality has always been an important theme in Asian cultures, a more common theme in Buddhist texts has been the closely related notion of universal friendship, that is, friendship toward all sentient beings, without exception. The opposite of friendship, of course, is enmity or ...

OBJECTIVES This study explored the relative contributions of friends and family to the social and emotional well-being of women and men in the first 2-6 months following the death of their spouse or partner. METHODS Three hundred and twenty-eight widowed men (39%) and women aged 50 and older completed self-administered questionnaires that included measures of contact and satisfaction with fri...

Our friends have more friends than we do. That is the basis of the friendship paradox. In mathematical terms, the mean number of friends of friends is higher than the mean number of friends. In the present study, we analyzed the relationship between the mean degree of vertices (individuals), 〈k〉, and the mean number of friends of friends, 〈kFF 〉, in scale-free networks with degrees ranging from...