Preferential attachment in the growth of social networks: the case of Wikipedia

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with that of the World Wide Web, despite the very different growth mechanism. In particular we measure a scale--invariant distribution of the in-- and out-- degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users can act globally on the network.Comment: 4 pages, 4 figures, revte

Forecasting audience increase on YouTube

User profiles constructed on Social Web platforms are often motivated by the need to maximise user reputation within a community. Subscriber, or follower, counts are an indicator of the influence and standing that the user has, where greater values indicate a greater perception or regard for what the user has to say or share. However, at present there lacks an understanding of the factors that lead to an increase in such audience levels, and how a user’s behaviour can a!ect their reputation. In this paper we attempt to fill this gap, by examining data collected from YouTube over regular time intervals. We explore the correlation between the subscriber counts and several behaviour features - extracted from both the user’s profile and the content they have shared. Through the use of a Multiple Linear Regression model we are able to forecast the audience levels that users will yield based on observed behaviour. Combining such a model with an exhaustive feature selection process, we yield statistically significant performance over a baseline model containing all features

Decompositions of Triangle-Dense Graphs

High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense, radius 2 subgraphs. This result quantifies the extent to which triangle-dense graphs resemble unions of cliques. We also show that our algorithm recovers planted clusterings in approximation-stable k-median instances.Comment: 20 pages. Version 1->2: Minor edits. 2->3: Strengthened {\S}3.5, removed appendi

Finding Cliques in Social Networks: A New Distribution-Free 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 adjacent. Our most basic definition is that of a c-closed graph, where for every pair of vertices u,v with at least c common neighbors, u and v are adjacent. We study the classic problem of enumerating all maximal cliques, an important task in social network analysis. We prove that this problem is fixed-parameter tractable with respect to c on c-closed graphs. Our results carry over to weakly c-closed graphs, which only require a vertex deletion ordering that avoids pairs of non-adjacent vertices with c common neighbors. Numerical experiments show that well-studied social networks tend to be weakly c-closed for modest values of c

Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear

Detecting and generating overlapping nested communities

Nestedness has been observed in a variety of networks but has been primarily viewed in the context of bipartite networks. Numerous metrics quantify nestedness and some clustering methods identify fully nested parts of graphs, but all with similar limitations. Clustering approaches also fail to uncover the overlap between fully nested subgraphs, as they assign vertices to a single group only. In this paper, we look at the nestedness of a network through an auxiliary graph, in which a directed edge represents a nested relationship between the two corresponding vertices of the network. We present an algorithm that recovers this so-called community graph, and finds the overlapping fully nested subgraphs of a network. We also introduce an algorithm for generating graphs with such nested structure, given by a community graph. This algorithm can be used to test a nested community detection algorithm of this kind, and potentially to evaluate different metrics of nestedness as well. Finally, we evaluate our nested community detection algorithm on a large variety of networks, including bipartite and non-bipartite ones, too. We derive a new metric from the community graph to quantify the nestedness of both bipartite and non-bipartite networks

Interpersonal interactions and human dynamics in a large social network

Abstract We study a large social network consisting of over 10 6 individuals, who form an Internet community and organize themselves in groups of different sizes. On the basis of the users' list of friends and other data registered in the database we investigate the structure and time development of the network. The structure of this friendship network is very similar to the structure of different social networks. However, here a degree distribution exhibiting two scaling regimes, power-law for low connectivity and exponential for large connectivity, was found. The groups size distribution and distribution of number of groups of an individual have power-law form. We found very interesting scaling laws concerning human dynamics. Our research has shown how long people are interested in a single task.

Remaining popular: power-law regularities in network dynamics

Abstract The structure of networks has been a focal research topic over the past few decades. These research efforts have enabled the discovery of numerous structural patterns and regularities, bringing forth advancements in many fields. In particular, the ubiquitous power-law patterns evident in degree distributions, graph eigenvalues and human mobility patterns have provided the opportunity to model many different complex systems. However, regularities in the dynamical patterns of networks remain a considerably less explored terrain. In this study we examine the dynamics of networks, focusing on stability characteristics of node popularity, and present our results using various empirical datasets. Specifically, we address several intriguing questions – for how long are popular nodes expected to remain so? How much time is expected to pass between two consecutive popularity periods? What characterizes nodes which manage to maintain their popularity for long periods of time? Surprisingly, we find that such temporal aspects are governed by a power-law regime, and that these power-law regularities are equally likely across all node ages