We present an in-depth study of co-following on Twitter based on the observation that two Twitter users whose followers have similar friends are also similar, even though they might not share any direct links or a single mutual follower. We show how this observation contributes to (i) a better understanding of language-agnostic user classification on Twitter, (ii) eliciting opportunities for Computational Social Science, and (iii) improving online marketing by identifying cross-selling opportunities. We start with a machine learning problem of predicting a user's preference among two alternative choices of Twitter friends. We show that co-following information provides strong signals for diverse classification tasks and that these signals persist even when (i) the most discriminative features are removed and (ii) only relatively "sparse" users with fewer than 152 but more than 43 Twitter friends are considered. Going beyond mere classification performance optimization, we present applications of our methodology to Computational Social Science. Here we confirm stereotypes such as that the country singer Kenny Chesney (@kennychesney) is more popular among @GOP followers, whereas Lady Gaga (@ladygaga) enjoys more support from @TheDemocrats followers. In the domain of marketing we give evidence that celebrity endorsement is reflected in co-following and we demonstrate how our methodology can be used to reveal the audience similarities between Apple and Puma and, less obviously, between Nike and Coca-Cola. Concerning a user's popularity we find a statistically significant connection between having a more "average" followership and having more followers than direct rivals. Interestingly, a audience also seems to be linked to a audience in terms of their co-following.
@cite_4: Uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman [Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002)] and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom [Proc. Natl. Acad. Sci. U.S.A. 104, 7327 (2007); Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008)], [J. Stat. Mech.: Theory Exp. (2008), P10008], and Ronhovde and Nussinov [Phys. Rev. E 80, 016109 (2009)] have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.
@cite_7: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i.e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e.g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
@cite_29: A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and there fore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.
@cite_0: Many networks of interest in the sciences, including social networks, computer networks, and metabolic and regulatory networks, are found to divide naturally into communities or modules. The problem of detecting and characterizing this community structure is one of the outstanding issues in the study of networked systems. One highly effective approach is the optimization of the quality function known as “modularity” over the possible divisions of a network. Here I show that the modularity can be expressed in terms of the eigenvectors of a characteristic matrix for the network, which I call the modularity matrix, and that this expression leads to a spectral algorithm for community detection that returns results of demonstrably higher quality than competing methods in shorter running times. I illustrate the method with applications to several published network data sets.
@cite_12: The detection of the community structure in networks is beneficial to understand the network structure and to analyze the network properties. Based on node similarity, a fast and efficient method for detecting community structure is proposed, which discovers the community structure by iteratively incorporating the community containing a node with the communities that contain the nodes with maximum similarity to this node to form a new community. The presented method has low computational complexity because of requiring only the local information of the network, and it does not need any prior knowledge about the communities and its detection results are robust on the selection of the initial node. Some real-world and computer-generated networks are used to evaluate the performance of the presented method. The simulation results demonstrate that this method is efficient to detect community structure in complex networks, and the ZLZ metrics used in the proposed method is the most suitable one among local indices in community detection.
Our mapping and visualization of similar accounts in is conceptually similar to community detection which also identifies groups of related accounts. Classical community detection looks at the global network and tries to find areas with unusually high triadic closure @cite_0 or otherwise unusual linkage patterns. A survey of the area and experimental comparisons can be found in @cite_7 and @cite_4 respectively. Related are notions of graph centrality that also require the whole graph @cite_29 . The approach in @cite_12 is arguably the most similar to ours as it combines local structural information with node similarity in an iterative manner. The similarity used, however, requires direct co-links and even direct links. Our approach differs in a number of ways. First, we are not interesting in clustering grouping users but only understand the relative positions of main ones. Second, we do not require a global view of the network but, in return, we cannot argue about things such as node centrality or PageRank. Third, we do not want to find communities induced by friends-of-friends type links. Rather we strive for a similarity-only based approach that can easily be transferred to domains without any friends-of-friend links.