Related papers: Friendship paradox disappears under degree biased …

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…

We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…

Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections.…

Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…

Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…

In this paper, we study diffusion social learning over weakly-connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some…

We study a number of graph exploration problems in the following natural scenario: an algorithm starts exploring an undirected graph from some seed node; the algorithm, for an arbitrary node $v$ that it is aware of, can ask an oracle to…

We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…

We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter $ \alpha$. We prove that, with high probability, the node degrees satisfy the following ordering property: the…

In several scale free graph models the asymptotic degree distribution and the characteristic exponent change when only a smaller set of vertices is considered. Looking at the common properties of these models, we present sufficient…

Many complex networks display strong heterogeneity in the degree (connectivity) distribution. Heterogeneity in the degree distribution often reduces the average distance between nodes but, paradoxically, may suppress synchronization in…

We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…

In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…

A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the node's neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks,…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…

Rather than anonymizing social graphs by generalizing them to super nodes/edges or adding/removing nodes and edges to satisfy given privacy parameters, recent methods exploit the semantics of uncertain graphs to achieve privacy protection…

Across income groups and countries, individual citizens perceive economic inequality spectacularly wrong. These misperceptions have far-reaching consequences, as it is perceived inequality, not actualinequality informing redistributive…