Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Sparse matrix computations for dynamic network centrality.

Abstract: Time sliced networks describing human-human digital interactions are typically large and sparse This is the case, for example, with pairwise connectivity describing social media, voice call or physical proximity, when measured over seconds, minutes or hours However, if we wish to quantify and compare the overall time-dependent centrality of the network nodes, then we should account for the global flow of information through time Because the time-dependent edge structure typically allows information to diffuse widely around the network, a natural summary of sparse but dynamic pairwise interactions will generally take the form of a large dense matrix For this reason, computing nodal centralities for a time-dependent network can be extremely expensive in terms of both computation and storage; much more so than for a single, static network In this work, we focus on the case of dynamic communicability, which leads to broadcast and receive centrality measures We derive a new algorithm for computing time-dependent centrality that works with a sparsified version of the dynamic communicability matrix In this way, the computation and storage requirements are reduced to those of a sparse, static network at each time point The new algorithm is justified from first principles and then tested on a large scale data set We find that even with very stringent sparsity requirements (retaining no more than ten times the number of nonzeros in the individual time slices), the algorithm accurately reproduces the list of highly central nodes given by the underlying full system This allows us to capture centrality over time with a minimal level of storage and with a cost that scales only linearly with the number of time points We also describe and test three variants of the proposed algorithm that require fewer parameters and achieve a further reduction in the computational cost

Latent Network Features and Overlapping Community Discovery via Boolean Intersection Representations

Abstract: We propose a new latent Boolean feature model for complex networks that capture different types of node interactions and network communities. The model is based on a new concept in graph theory, termed the Boolean intersection representation of a graph, which generalizes the notion of an intersection representation. We mostly focus on one form of Boolean intersection, termed cointersection , and describe how to use this representation to deduce node feature sets and their communities. We derive several general bounds on the minimum number of features used in cointersection representations and discuss graph families for which exact cointersection characterizations are possible. Our results also include algorithms for finding optimal and approximate cointersection representations of a graph.

Using centrality algorithms on directed graphs for synonym expansion

Abstract: This paper presents our explorations in using graph centrality measures to solve the synonym expansion problem. In particular, we use the concept of directional similarity to derive directed graphs on which we apply centrality algorithms to identify the most likely synonyms for a target word in a given context. We show that our method can lead to performance comparable to the state-of-the-art.

Analyzing the propagation of influence and concept evolution in enterprise social networks through centrality and latent semantic analysis

Abstract: Understanding the propagation of influence and the concept flow over a network in general has profound theoretical and practical implications. In this paper, we propose a novel approach to ranking individual members of a real-world communication network in terms of their roles in such propagation processes. We first improve the accuracy of the centrality measures by incorporating temporal attributes. Then, we integrate weighted PageRank and centrality scores to further improve the quality of these measures. We valid these ranking measures through a study of an email archive of a W3C working group against an independent list of experts. The results show that time-sensitive Degree, time-sensitive Betweenness and the integration of the weighted PageRank and these centrality measures yield the best ranking results. Our approach partially solves the rank sink problem of PageRank by adjusting flexible jumping probabilities with Betweenness centrality scores. Finally the text analysis based on Latent Semantic Indexing extracts key concepts distributed in different time frames and explores the evolution of the discussion topics in the social network. The overall study depicts an overview of the roles of the actors and conceptual evolution in the social network. These findings are important to understand the dynamics of the social networks.

Optimal navigation for characterizing the role of the nodes in complex networks

Abstract: In this paper, we explore how the approach of optimal navigation (Cajueiro (2009) [33] ) can be used to evaluate the centrality of a node and to characterize its role in a network. Using the subway network of Boston and the London rapid transit rail as proxies for complex networks, we show that the centrality measures inherited from the approach of optimal navigation may be considered if one desires to evaluate the centrality of the nodes using other pieces of information beyond the geometric properties of the network. Furthermore, evaluating the correlations between these inherited measures and classical measures of centralities such as the degree of a node and the characteristic path length of a node, we have found two classes of results. While for the London rapid transit rail, these inherited measures can be easily explained by these classical measures of centrality, for the Boston underground transportation system we have found nontrivial results.