Related papers: Friendship paradox disappears under degree biased …
The friendship paradox states that your friends have on average more friends than you have. Does the paradox "hold" for other individual characteristics like income or happiness? To address this question, we generalize the friendship…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
How popular a topic or an opinion appears to be in a network can be very different from its actual popularity. For example, in an online network of a social media platform, the number of people who mention a topic in their posts---i.e., its…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be…
In this paper, we study a bipartite analogue of the `random graphs evolving by degrees' process. We are given a bipartitioned set of vertices $V$ into two disjoint parts ${L}$ and ${R}$ and possibly unequal positive constants $\alpha$ and…
The "friendship paradox" (Feld1991) refers to the fact that, on average, people have strictly fewer friends than their friends have. I show that this over-sampling of the most popular people amplifies behaviors that involve…
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
The friendship paradox -- the observation that, on average, one's friends have more friends than oneself -- admits two common formulations depending on whether averaging is performed over edges or over nodes. These two definitions, the…
The friendship paradox states that, on average, our friends have more friends than we do. In network terms, the average degree over the nodes can never exceed the average degree over the neighbours of nodes. This effect, which is a classic…
This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for?…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the…