Network motifs are patterns of over-represented node interactions in a network which have been previously used as building blocks to understand various aspects of the social networks. In this paper, we use motif patterns to characterize the information diffusion process in social networks. We study the lifecycle of information cascades to understand what leads to saturation of growth in terms of cascade reshares, thereby resulting in expiration, an event we call diffusion inhibition''. In an attempt to understand what causes inhibition, we use motifs to dissect the network obtained from information cascades coupled with traces of historical diffusion or social network links. Our main results follow from experiments on a dataset of cascades from the Weibo platform and the Flixster movie ratings. We observe the temporal counts of 5-node undirected motifs from the cascade temporal networks leading to the inhibition stage. Empirical evidences from the analysis lead us to conclude the following about stages preceding inhibition: (1) individuals tend to adopt information more from users they have known in the past through social networks or previous interactions thereby creating patterns containing triads more frequently than acyclic patterns with linear chains and (2) users need multiple exposures or rounds of social reinforcement for them to adopt an information and as a result information starts spreading slowly thereby leading to the death of the cascade. Following these observations, we use motif based features to predict the edge cardinality of the network exhibited at the time of inhibition. We test features of motif patterns by using regression models for both individual patterns and their combination and we find that motifs as features are better predictors of the future network organization than individual node centralities.
In this paper, we use network features in the stages preceding inhibition to predict the attributes of the inhibition network structure of cascades. Such problems of structure prediction has been a subject of research mainly from a diffusion network inference perspective @cite_39 . Using topological features of the network structure has been used in @cite_4 to predict the future links of the network. In this paper, we adopt motif based network features to observe whether the motifs' appearances are indicators of how the nodes would organize themselves to form the network during inhibition.
@cite_4 @cite_39
2092129584 2950143436 1587790278 2953249628
The analysis of network connections, diffusion processes and cascades requires evaluating properties of the diffusion network. Properties of interest often involve variables that are not explicitly observed in real world diffusions. Connection strengths in the network and diffusion paths of infections over the network are examples of such hidden variables. These hidden variables therefore need to be estimated for these properties to be evaluated. In this paper, we propose and study this novel problem in a Bayesian framework by capturing the posterior distribution of these hidden variables given the observed cascades, and computing the expectation of these properties under this posterior distribution. We identify and characterize interesting network diffusion properties whose expectations can be computed exactly and efficiently, either wholly or in part. For properties that are not nice' in this sense, we propose a Gibbs Sampling framework for Monte Carlo integration. In detailed experiments using various network diffusion properties over multiple synthetic and real datasets, we demonstrate that the proposed approach is significantly more accurate than a frequentist plug-in baseline. We also propose a map-reduce implementation of our framework and demonstrate that this can analyze cascades with millions of infections in minutes. Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures from these observed cascades? What kind of cascades and how many cascades do we need? Are there some network structures which are more difficult than others to recover? Can we design efficient inference algorithms with provable guarantees? Despite the increasing availability of cascade data and methods for inferring networks from these data, a thorough theoretical understanding of the above questions remains largely unexplored in the literature. In this paper, we investigate the network structure inference problem for a general family of continuous-time diffusion models using an @math -regularized likelihood maximization framework. We show that, as long as the cascade sampling process satisfies a natural incoherence condition, our framework can recover the correct network structure with high probability if we observe @math cascades, where @math is the maximum number of parents of a node and @math is the total number of nodes. Moreover, we develop a simple and efficient soft-thresholding inference algorithm, which we use to illustrate the consequences of our theoretical results, and show that our framework outperforms other alternatives in practice. Learning about the structure of hidden or covert networks is a major challenge in epidemiology, sociology, and intelligence analysis. Vertices in hidden networks usually cannot be enumerated or sampled in a systematic way; they can only be revealed by tracing links emanating from already-observed vertices. Observers sometimes cannot follow links directly, and instead must rely on passive observation of a dynamic process to reveal vertices and edges. This paper outlines a framework for estimating network structures from partial observation of information diffusion through the network. Diffusion is modeled by a continuous-time Markov epidemic model. Edges are revealed by transmission events and new vertices are uncovered when information is transmitted to them. The approach is a generalization of tools developed to reconstruct drug-user networks from respondent-driven sampling studies in epidemiology. The likelihood of the diffusion process can be interpreted as an exponential random graph model. A Bayesian method for probabilistic reconstruction of the transmission-induced subgraph is described. We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in its neighborhood. We introduce a topological property known as r-robustness of a graph, and show that this property provides improved bounds on tolerating malicious behavior, in comparison to traditional concepts such as connectivity and minimum degree. We use this topological property to analyze the canonical problems of distributed consensus and broadcasting, and provide sufficient conditions for these operations to succeed. Finally, we provide a construction for r-robust graphs and show that the common preferential-attachment model for scale-free networks produces a robust graph.