Related papers: The friendship paradox in real and model networks
According to the small-world concept, the entire world is connected through short chains of acquaintances. In popular imagination this is captured in the phrase six degrees of separation, implying that any two individuals are, at most, six…
In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist,…
With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has…
In many real-world networks, relationships often go beyond simple dyadic presence or absence; they can be positive, like friendship, alliance, and mutualism, or negative, characterized by enmity, disputes, and competition. To understand the…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
The observation that individuals tend to be friends with people who are similar to themselves, commonly known as homophily, is a prominent and well-studied feature of social networks. Many machine learning methods exploit homophily to…
This paper develops strategic foundations for an important statistical model of random networks with heterogeneous expected degrees. Based on this, we show how social networking services that subtly alter the costs and indirect benefits of…
In considering a social network, there are cases where people is transferred to another place. Then the physical (direct) relations among nodes are lost by the movement. In terms of a network theory, some nodes break the present connections…
In social networks, it is conventionally thought that two individuals with more overlapped friends tend to establish a new friendship, which could be stated as homophily breeding new connections. While the recent hypothesis of maximum…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon?…
A study of the dynamical formation of networks of friends and enemies in social media, in this case Twitter, is presented. We characterise the single node properties of such networks, as the clustering coefficient and the degree, to…
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…
In Hazra, den Hollander and Parvaneh (2025) we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distribution of the friendship biases between vertices and their…
The study of networks has received increased attention recently not only from the social sciences and statistics but also from physicists, computer scientists and mathematicians. One of the principal problem in networks is community…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
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…
Although the origin of the fat-tail characteristic of the degree distribution in complex networks has been extensively researched, the underlying cause of the degree distribution characteristic across the complete range of degrees remains…
Conventional graph neural networks (GNNs) are often confronted with fairness issues that may stem from their input, including node attributes and neighbors surrounding a node. While several recent approaches have been proposed to eliminate…