We propose a model of network formation in peer-to-peer networks, that allows us to observe their suseptibility to sybil attacks against routing security. Peers try to selfishly fulfill their communication needs, by connecting directly to communication partners (‘friends’) or indirectly through stranger nodes. We assess the strategies nodes will follow depending on the topology of the friendshi...

An L(2, 1)-labeling (or distance two labeling) of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x) − f(y)| ≥ 2 if d(x, y) = 1 and |f(x) − f(y)| ≥ 1 if d(x, y) = 2. The L(2, 1)-labeling number λ(G) of G is the smallest number k such that G has an L(2, 1)-labeling with max{f(v) : v ∈ V (G)} = k. In this paper we completely determine the λ-...

Let G = (V,E) be a simple connected graph. The eccentric-distance sum of G is defined as ξ(G) = ∑ {u,v}⊆V (G) [e(u) + e(v)]d(u, v), where e(u) is the eccentricity of the vertex u in G and d(u, v) is the distance between u and v. In this paper, we establish formulae to calculate the eccentric-distance sum for some graphs, namely wheel, star, broom, lollipop, double star, friendship, multi-star g...

A graph exhibits the small-world phenomenon if most nodes can be reached through a short chain of steps along the edges. Current small-world models include those based on a simple base graph structure, which is augmented with shortcuts added according to some random process. We examined the small-world graph models mentioned above with variable population density through computer simulations. F...

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Graphs are commonly used to model complex and large scaled structures. Friendship relations on a social platform, recommendations in big online marketplaces like e-bay or Amazon, or the link structure of the web, are examples for such structures. It is generally accepted (and appreciated) that these huge web structures tend to grow. But with a growing amount of stored data and higher complexity...

This article provides a qualitative analysis of the social interactions between Chinese and Tanzanian participants within joint Chinese-Tanzanian educational initiative in Confucius Institute programming at University Dar es Salaam. The addresses issue how people involved understand their those governments context increased presence sub-Saharan Africa. shows that friendships are motivated by bo...

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 ...

A friendship 3-hypergraph is a 3-hypergraph in which any 3 vertices, u, v and w, occur in pairs with a unique fourth vertex x; i.e., uvx, uwx, vwx are 3-hyperedges. S os found friendship 3-hypergraphs coming from Steiner Triple Systems. Hartke and Vandenbussche showed that any friendship 3-hypergraph can be decomposed into sets of K 4 's. We think of this as a set of 4-tuples and call it a frie...