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Ego-networks are fundamental structures in social graphs, yet the process of their evolution is still widely unexplored. In an online context, a key question is how link recommender systems may skew the growth of these networks, possibly…

Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…

We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one…

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

It is well known that differences in the average number of friends among social groups can cause inequality in the average wage and/or unemployment rate. However, the impact of social network structure on inequality is not evident. In this…

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…

Many online social networks are fundamentally directed, i.e., they consist of both reciprocal edges (i.e., edges that have already been linked back) and parasocial edges (i.e., edges that haven't been linked back). Thus, understanding the…

We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been…

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…

Being able to recommend links between users in online social networks is important for users to connect with like-minded individuals as well as for the platforms themselves and third parties leveraging social media information to grow their…

This paper considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating…

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with…

The key feature of online social networks (OSN) is the ability of users to become active, make friends and interact via comments, videos or messages with those around them. This social interaction is typically perceived as critical to the…

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…

Social networks have been of much interest in recent years. We here focus on a network structure derived from co-occurrences of people in traditional newspaper media. We find three clear deviations from what can be expected in a random…

The popularity of an opinion in one's direct circles is not necessarily a good indicator of its popularity in one's entire community. Network structures make local information about global properties of the group potentially inaccurate, and…

Non-centralized recommendation-based decision making is a central feature of several social and technological processes, such as market dynamics, peer-to-peer file-sharing and the web of trust of digital certification. We investigate the…

Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…

Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…