相关论文: Four Degrees of Separation

A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering. The circular separation dimension of a graph $G$, denoted by $\pi^\circ(G)$, is the…

For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we…

The friendship paradox refers to the sociological observation that, while the people's assessment of their own popularity is typically self-aggrandizing, in reality they are less popular than their friends. The generalized friendship…

All online sharing systems gather data that reflects users' collective behaviour and their shared activities. This data can be used to extract different kinds of relationships, which can be grouped into layers, and which are basic…

Inspired by Lelek's idea from [Disjoint mappings and the span of spaces, Fund. Math. 55 (1964), 199 -- 214], we introduce the novel notion of the span of graphs. Using this, we solve the problem of determining the \emph{maximal safety…

In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…

With a view on graph clustering, we present a definition of vertex-to-vertex distance which is based on shared connectivity. We argue that vertices sharing more connections are closer to each other than vertices sharing fewer connections.…

In an undirected social graph, a friendship link involves two users and the friendship is visible in both the users' friend lists. Such a dual visibility of the friendship may raise privacy threats. This is because both users can separately…

This paper is concerned with a stochastic model for the spread of kindness across a social network. Individuals are located on the vertices of a general finite connected graph, and are characterized by their kindness belief. Each…

The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the…

Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive…

We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…

For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $n$ and $k$ be two…

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…

We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits…

We study the distribution of diameters d of Erd\"os-R\'enyi random graphs with average connectivity c. The diameter d is the maximum among all shortest distances between pairs of nodes in a graph and an important quantity for all dynamic…

In recent years, a large body of research has demonstrated that judgments and behaviors can propagate from person to person. Phenomena as diverse as political mobilization, health practices, altruism, and emotional states exhibit similar…

The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…

Let $G$ be a graph with order $n(G)$, size $m(G)$, first Zagreb index $M_1(G)$, and second Zagreb index $M_2(G)$. More than twenty years ago, it was conjectured that $\frac{M_1(G)}{n(G)} \leq \frac{M_2(G)}{m(G)}$. Later, Hansen and…

Analyzing and mining students' behaviors and interactions from big data is an essential part of education data mining. Based on the data of campus smart cards, which include not only static demographic information but also dynamic…