Abstract. Cascading processes, such as disease contagion, viral marketing, and information diffusion, are a pervasive phenomenon in many types of networks. The problem of devising intervention strategies to facilitate or inhibit such processes has recently received considerable attention. However, a major challenge is that the underlying network is often unknown. In this paper, we revisit the problem of inferring latent network structure given observations from a diffusion process, such as the spread of trending topics in social media. We define a family of novel probabilistic models that can explain recurrent cascading behavior, and take into account not only the time differences between events but also a richer set of additional features. We show that MAP inference is tractable and can therefore scale to very large real-world networks. Further, we demonstrate the effectiveness of our approach by inferring the underlying network structure of a subset of the popular Twitter following network by analyzing the topics of a large number of messages posted by users over a 10-month period. Experimental results show that our models accurately recover the links of the Twitter network, and significantly improve the performance over previous models based entirely on time.

In many social networks, there exist two types of users that exhibit different influence and different behavior. For instance, statistics have shown that less than 1% of the Twitter users (e.g. entertainers, politicians, writers) produce 50% of its content [1], while the others (e.g. fans, followers, readers) have much less influence and completely different social behavior.In this paper, we define and explore a novel problem called community kernel detection in order to uncover the hidden community structure in large social networks. We discover that influential users pay closer attention to those who are more similar to them, which leads to a natural partition into different community kernels.We propose GREEDY and WEBA, two efficient algorithms for finding community kernels in large social networks. GREEDY is based on maximum cardinality search, while WEBA formalizes the problem in an optimization framework. We conduct experiments on three large social networks: Twitter, Wikipedia, and Coauthor, which show that WEBA achieves an average 15%-50% performance improvement over the other state-of-the-art algorithms, and WEBA is on average 6-2,000 times faster in detecting community kernels.

Connectivity and capacity are two measures for the performance of mobile ad hoc networks that have been studied extensively under standard point-to-point physical layer assumptions. However, extensive recent research at the physical layer has demonstrated the improvement in performance possible when multiple radios concurrently transmit in the same radio channel. In this paper, we consider how such physical layer cooperation improves the connectivity in wireless ad hoc networks. In particular, with noncoherent cooperation at the physical layer, we consider conditions on the node density λ (or, equivalently, the transmit power) for full connectivity and percolation for large networks in various dimensions and with various path loss exponents α. For one-dimensional (1-D) extended networks, in sharp contrast to noncooperative networks, we demonstrate that full connectivity can be realized under certain conditions. In particular, for any node density with α < 1, or for node density λ > 2 when α = 1, full connectivity occurs with probability one. Conversely, we demonstrate that, under noncoherent cooperation, there is no full connectivity with probability one when α > 1. In two-dimensional (2-D) extended networks with noncoherent cooperation, for any node density with α < 2, or for node density λ > 5 when α = 2, full connectivity is achieved. Conversely, there is no full connectivity with probability one when α > 2, but we prove that, for α 4, the percolation threshold of the noncoherent cooperative network is strictly less than that of the noncooperative network. Analogous results are presented for dense networks. Hence, the main conclusion is that even relatively simple physical layer cooperation in the form of noncoherent power summing can substantially improve the connectivity of large ad hoc networks.

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In this paper, we establish the definition of community fundamentally different from what was commonly accepted in previous studies, where communities were typically assumed to be densely connected internally but sparsely connected to the rest of the network. A community should be considered as a densely connected subset in which the probability of an edge between two randomly-picked vertices is higher than average. Moreover, a community should also be well connected to the remaining network, that is, the number of edges connecting a community to the rest of the graph should be significant. In order to identify a well-defined community, we provide rigorous definitions of two relevant terms: "whiskers" and the "core". Whiskers correspond to subsets of vertices that are barely connected to the rest of the network, while the core exclusively contains the type of community we are interested in. We have proven that detecting whiskers, or equivalently, extracting the core, is an NP-complete problem for weighted graphs. Then, three heuristic algorithms are proposed for finding an approximate core and are evaluated for their performance on large networks, which reveals the common existence of the core structure in both random and real-world graphs. Further, well-defined communities can be extracted from the core using a number of techniques, and the experimental results not only justify our intuitive notion of community, but also demonstrate the existence of large-scale communities in various complex networks.