Related papers: The friendship paradox in real and model networks
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Recent work has demonstrated that many social networks, and indeed many networks of other types also, have broad distributions of vertex degree. Here we show that this has a substantial impact on the shape of ego-centered networks, i.e.,…
We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the Majority Rule, applied…
We study social learning in which agents weight neighbors' opinions differently based on their degrees, capturing situations in which agents place more trust in well-connected individuals or, conversely, discount their influence. We derive…
The so-called rich-club phenomenon in a complex network is characterized when nodes of higher degree (hubs) are better connected among themselves than are nodes with smaller degree. The presence of the rich-club phenomenon may be an…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…
Long ties, the social ties that bridge different communities, are widely believed to play crucial roles in spreading novel information in social networks. However, some existing network theories and prediction models indicate that long ties…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
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…
On-line social networks (OSNs) often contain many different types of relationships between users. When studying the structure of OSNs such as Facebook, two of the most commonly studied networks are friendship and interaction networks. The…
In this paper, we propose a general model for collaboration networks. Depending on a single free parameter "{\bf preferential exponent}", this model interpolates between networks with a scale-free and an exponential degree distribution. The…
Many real world networks, such as social networks, are primarily formed through local interactions between agents. Additionally, in contrast with common network models, social and biological networks exhibit a high degree of clustering.…
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…
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…
We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and friendships, the degree distribution, path lengths,…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…