Counting Subgraphs in Relational Event Graphs

Mobile phone carriers face challenges from three synergistic dimensions: Wireless, social, and mobile. Despite significant advances that have been made about social networks and human mobility, respectively, our knowledge about the interplay between two layers remains largely limited, partly due to the difficulty in obtaining large-scale datasets that could offer at the same time social and mobile information across a substantial population over an extended period of time. In this paper, we take advantage of a massive, longitudinal mobile phone dataset that consists of human mobility and social network information simultaneously, allowing us to explore the impact of human mobility patterns on the underlying social network. We find that human mobility plays an important role in shaping both local and global structural properties of social network. In contrast to the lack of scale in social networks and human movements, we discovered a characteristic distance in physical space between 10 and 20 km that impacts both local clustering and modular structure in social network. We also find a surprising distinction in trajectory overlap that segments social ties into two categories. Our results are of fundamental relevance to quantitative studies of human behavior, and could serve as the basis of anchoring potential theoretical models of human behavior and building and developing new applications using social and mobile technologies.

Sentiment analysis research has focused on using text for predicting sentiments without considering the unavoidable peer influence on user emotions and opinions. The lack of large-scale ground-truth data on sentiments of users in social networks has limited research on how predictable sentiments are from social ties. In this paper, using a large-scale dataset on human sentiments, we study sentiment prediction within social networks. We demonstrate that sentiments are predictable using structural properties of social networks alone. With social science and psychology literature, we provide evidence on sentiments being connected to social relationships at four different network levels, starting from the ego-network level and moving up to the whole-network level. We discuss emotional signals that can be captured at each level of social relationships and investigate the importance of structural features on each network levels. We demonstrate that sentiment prediction that solely relies on social network structure can be as (or more) accurate than text-based techniques. For the situations where complete posts and friendship information are difficult to get, we analyze the trade-off between the sentiment prediction performance and the available information. When computational resources are limited, we show that using only four network properties, one can predict sentiments with competitive accuracy. Our findings can be used to (1) validate the peer influence on user sentiments, (2) improve classical text-based sentiment prediction methods, (3) enhance friend recommendation by utilizing sentiments, and (4) help identify personality traits.

We present new algorithms for a distributed model for graph computations motivated by limited information sharing we first discussed in [20]. Two or more independent entities have collected large social graphs. They wish to compute the result of running graph algorithms on the entire set of relationships. Because the information is sensitive or economically valuable, they do not wish to simply combine the information in a single location. We consider two models for computing the solution to graph algorithms in this setting: 1) limited-sharing: the two entities can share only a polylogarithmic size subgraph; 2) low-trust: the entities must not reveal any information beyond the query answer, assuming they are all honest but curious. We believe this model captures realistic constraints on cooperating autonomous data centers. We have algorithms in both setting for s - t connectivity in both models. We also give an algorithm in the low-communication model for finding a planted clique. This is an anomaly- detection problem, finding a subgraph that is larger and denser than expected. For both the low- communication algorithms, we exploit structural properties of social networks to prove perfor- mance bounds better than what is possible for general graphs. For s - t connectivity, we use known properties. For planted clique, we propose a new property: bounded number of triangles per node. This property is based upon evidence from the social science literature. We found that classic examples of social networks do not have the bounded-triangles property. This is because many social networks contain elements that are non-human, such as accounts for a business, or other automated accounts. We describe some initial attempts to distinguish human nodes from automated nodes in social networks based only on topological properties.

CENTERS OF TRIANGULATED GRAPHS V. D. Chepoi Let G = (X, U) be an ordinary graph with arbitrarily (not necessarily finitely) many vertexes, any two of which are joined by some finite chain. We endow G with a standard metric d(x, y) equal to the number of edges in the chain of shortest length joining vertexes x, y. The eccentricity e(z) of a vertex z is defined as {d(z, v): v e X}. The radius r(G) is the least eccentricity of the vertexes, and the diameter d(G) is the largest eccentricity. The center C(G) of G is the subgraph generated by the set of vertexes with minimal eccentricity. It is well known [I, 2] that any graph G, even if it is not connected, is the center of some graph G', i.e., G = C(G'). At the same time, if one confines attention to special classes of graphs, their centers may have rather specific features. Thus, a well-known re- sult of Jordan [3] states that the center of any finite tree consists of one vertex or two adjacent vertexes; that is to say, the only two possibilities are the graphs K l and K 2 (where K n denotes the complete subgraph on n vertexes). The centers of maximal outerplanar graphs and 2-trees were described in [4, 5]. In this paper we characterize the centers of triangu- lated graphs. In this connection, we note that metric properties, including in particular properties of the centers, of triangulated graphs have been studied by various authors [6-9]. Our Theorems 1 and 2 were proved in [8], but they are established here in a more general form and the proofs are simpler. Recall [i0] that a graph G is said to be triangulated if, in any simple cycle F of length more than 3, there are two vertexes not adjacent in r but joined by an edge in G. Recall moreover that a clique of a graph G is any maximal complete subgraph (with re- spect to inclusion). The density of a graph G is the cardinality of the largest clique in G (if such a clique exists). Throughout this paper, the term triangulated graph will mean a triangulated graph of finite diameter without infinite complete subgraphs. Let CT denote the family of graphs which are centers of triangulated graphs. We shall need a number of additional concepts and definitions. Given sets M c X in a graph G and any number r ~ 0, we put where

Assessing the stability of a clustering method involves the measurement of the extent to which the generated clusters are affected by perturbations in the input data. A measure which specifies the disturbance in a set of clusters as the minimum number of operations required to restore the set of modified clusters to the original ones is adopted. A number of well-known graph theoretic clustering methods are compared in terms of their stability as determined by this measure. Specifically, it is shown that among the clustering methods in any of several families of graph theoretic methods, clusters defined as the connected components are the most stable and the clusters specified as the maximal complete subgraphs are the least stable. Furthermore, as one proceeds from the method producing the most narrow clusters (maximal complete subgraphs) to those producing relatively broader clusters, the clustering process is shown to remain at least as stable as any method in the previous stages. Finally, the lower and the upper bounds for the measure of stability, when clusters are defined as the connected components, are derived.

Dyad and triad census summarize much of the network level structural information of a given directed network. They have been found very useful in analyzing structural properties of social networks. This study aims to explore crisis communication network by following dyad and triad census analysis approach to investigate the association of microlevel communication patterns with organizational crisis. This study further tests hypothesis related to the process of data generation and tendency of the structural pattern of transitivity using dyad and triad census output. The changing communication network at Enron Corporation during the period of its crisis is analyzed in this study. Significant differences in the presence of different isomorphism classes or microlevel patterns of both dyad and triad census are noticed in crisis and non-crisis period network of Enron email corpus. It is also noticed that crisis communication network shows more transitivity compared to the non-crisis communication network.

In this paper we introduce a novel scheme for key management in social networks that is a first step towards the creation of a private social network. A social network graph (i.e., the graph of friendship relationships) is private and social networks are often used to share content, which may be private, amongst its users. In the status quo, the social networking server has access to both this graph and to all of the content, effectively requiring that it is a trusted third party. The goal of this paper is to produce a mechanism through which users can control how their content is shared with other users, without relying on a trusted third party to manage the social network graph and the users' data. The specific access control model considered here is that users will specify access policies based on distance in the social network; for example some content is visible to friends only, while other content is visible to friends of friends, etc. This access control is enforced via key management. That is for each user, there is a key that only friends should be able to derive, there is a key that both friends of the user and friends of friends can derive, etc. The proposed scheme enjoys the following properties: i) the scheme is asynchronous in that it does not require users to be online at the same time, ii) the scheme provides key indistinguishability (that is if a user is not allowed to derive a key according to the access policy, then that key is indistinguishable from a random value), iii) the scheme is efficient in terms of server storage and key derivation time, and iv) the scheme is collusion resistant.

Covering all cliques of a graph

A social network is a collection of social entities and the relations among them. Collection and sharing of such network data for analysis raise significant privacy concerns for the involved individuals, especially when human users are involved. To address such privacy concerns, several techniques, such as k-anonymity based approaches, have been proposed in the literature. However, such approaches introduce a large amount of distortion to the original social network graphs, thus raising serious questions about their utility for useful social network analysis. Consequently, these techniques may never be applied in practice. In this paper, we emphasize the use of network structural semantics in the social network analysis theory to address this problem. We propose an approach for enhancing anonymization techniques that preserves the structural semantics of the original social network by using the notion of roles and positions. We present experimental results that demonstrate that our approach can significantly help in preserving graph and social network theoretic properties of the original social networks, and hence improve utility of the anonymized data.

The compatibility relation occurs in many different disciplines in science and engineering. When a compatibility relation exists between pairs of elements in a set, an important problem is to derive the collection of aU those elements that form maximal compatibles. If the set of elements with the compatibility relation can be visualized as a compatibility graph of which the different nodes represent the elements of the set, the only edges of the graph being the nonoriented lines joining pairs of elements with the compatibility relation, then the problem of deriving the maximal compatibles becomes identical to the graph theory problem of finding all the maximal complete subgraphs in a symmetric graph. Recently, in connection with simplifying incompletely specified sequential machines, where a kind of compatibility relation also exists between pairs of internal states, Das and Sheng proposed a method for deriving the different maximal compatibles through finding all of the modified cut-sets of the incompatibility graph of the machine. This paper, without confining itself to only incompletely specified machines, considers the problem involving the compatibility relation in a broader perspective and suggests a new approach for finding aU the modified cut-sets of the incompatibility graph of a set having a compatibility relation between its different pairs of elements.

Network biology integrates different kinds of data, including physical or functional networks and disease gene sets, to interpret human disease. A clique (maximal complete subgraph) in a protein-protein interaction network is a topological module and possesses inherently biological significance. A disease-related clique possibly associates with complex diseases. Fully identifying disease components in a clique is conductive to uncovering disease mechanisms. This paper proposes an approach of predicting disease proteins based on cliques in a protein-protein interaction network. To tolerate false positive and negative interactions in protein networks, extending cliques and scoring predicted disease proteins with gene ontology terms are introduced to the clique-based method. Precisions of predicted disease proteins are verified by disease phenotypes and steadily keep to more than 95%. The predicted disease proteins associated with cliques can partly complement mapping between genotype and phenotype, and provide clues for understanding the pathogenesis of serious diseases.

Methods. The main methods of research are: comparative analysis of existing business models of advertising, grouping data to evaluate them – in systematizing and summarizing research results, as well as informal (intuitive) forecasting methods – when forming a sample for observation and analysis of trends in the formation of business models of advertising. Results. The work is devoted to the study of modern tools for advertising works, goods, services through social networks. The purpose of the study is to determine the trends in the formation of business models for the advertising activities of legal entities in social networks. The main task is to study the tools for promoting goods / services in social networks, increasing loyalty through social networks. The article presents the results of the analysis of trends in the formation of business models of advertising activities of legal entities in social networks. It is shown how a change in the factors of the economy of sustainable development, in particular the age distribution of the population, affects the formation of the advertising policy of a business entity. The contradiction between the meaning of the concept of «social network» and the peculiarities of the organization of advertising activities of legal entities is determined. The role of modern IT technologies, such as the Metauniverse, chat-bot, automated sales funnels and the use of artificial intelligence systems to solve the indicated contradictions, is shown. An attempt was made to evaluate the economic efficiency of using modern tools to form consumer loyalty to the activities of legal entities through social networks by giving the latter the features of socially adapted market entities. Novelty. The paper stresses the necessity of studying modern definitions of «social network», «economic entity and its avatar in a social network». The next step in the development of scientific thought should be the understanding, scientific justification and study of the differences between an individual and his image in the Internet space. Practical value. In accordance with global trends in the institutional protection of consumer personal data on the internet, the expected changes in the behavior of business entities in social networks and the role of technology companies in this process are shown. The indicated trends will objectively influence both the organizational structure of a business entity and the formation of business models of B2C interaction. The results of the study are of interest both to representatives of medium and large businesses, and to the scientific community for the formation of a theoretical scientific basis for modern advertising processes.

In order to prevent the disclosure of privacy-sensitive data, such as names and relations between users, social network graphs have to be anonymised before publication. Naive anonymisation of social network graphs often consists in deleting all identifying information of the users, while maintaining the original graph structure. Various types of attacks on naively anonymised graphs have been developed. Active attacks form a special type of such privacy attacks, in which the adversary enrols a number of fake users, often called sybils, to the social network, allowing the adversary to create unique structural patterns later used to re-identify the sybil nodes and other users after anonymisation. Several studies have shown that adding a small amount of noise to the published graph already suffices to mitigate such active attacks. Consequently, active attacks have been dubbed a negligible threat to privacy-preserving social graph publication. In this paper, we argue that these studies unveil shortcomings of specific attacks, rather than inherent problems of active attacks as a general strategy. In order to support this claim, we develop the notion of a robust active attack, which is an active attack that is resilient to small perturbations of the social network graph. We formulate the design of robust active attacks as an optimisation problem and we give definitions of robustness for different stages of the active attack strategy. Moreover, we introduce various heuristics to achieve these notions of robustness and experimentally show that the new robust attacks are considerably more resilient than the original ones, while remaining at the same level of feasibility.

Managers and group leaders of a community may not have enough information to help them direct the community development. In this paper, we adopt social network analysis, graph theory and data mining techniques to analyze groups in a community at their different project periods. Each group is presented by several attributes that are computed from social network analysis and graph theory to represent various interactions of the group members. The evolution of these attributes enables the discovery of the interaction patterns of different groups in their life cycles. With these discoveries, team leaders can obtain concise information about their teams' performance, and community managers can cluster groups to capture stereotypes of virtual teams in the community. Such knowledge will benefit group development in a community.

Entities in social networks may be subject to consolidation when they are inconsistently indexed, and subject to splitting when multiple entities share the same name. How much do errors or shortfalls in entity disambiguation distort network properties? We show empirically how network analysis results and derived implications can tremendously change depending solely on entity resolution techniques. We present a series of controlled experiments where we vary disambiguation accuracy to study error propagation and the robustness of common network metrics, topologies and key players. Our results suggest that for email data, not conducting deduplication, e.g. when operating on the level of email addressed instead of individuals, can make organizational communication networks appear to be less coherent and integrated as well as bigger than they truly are. For co-publishing networks, improper merging as caused by the commonly used initial based disambiguation techniques can make a scientific sector seem more dense and cohesive than it really is, and individual authors appear to be more productive, collaborative and diversified than they actually are. Disambiguation errors can also lead to the false detection of power law distributions of node degree; suggesting preferential attachment processes that might not apply.