Preventing Unraveling in Social Networks: The Anchored k-Core Problem

Bhawalkar, Kshipra; Kleinberg, Jon; Lewi, Kevin; Roughgarden, Tim; Sharma, Aneesh

doi:10.1007/978-3-642-31585-5_40

Cited by 23 publications

(14 citation statements)

References 14 publications

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“…Thus, to systematically exclude low-degree genes from permutation, we decided to use only genes in the 2-core of the protein-protein interaction network. A k - core of a network is a maximal group of nodes, all of which are connected to at least k other nodes in the network (Bhawalkar et al, 2012). This approach improves the observed distribution of p cent values.…”

Section: Methods and Resourcesmentioning

confidence: 99%

Pathway centrality in protein interaction networks identifies functional mediators of pulmonary disease

Park

Hescott

Slonim

2017

Preprint

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SummaryIdentification of functional pathways mediating molecular responses may lead to better understanding of disease processes and suggest new therapeutic approaches. We introduce a method to detect such mediating functions using topological properties of protein-protein interaction networks. We introduce the concept of pathway centrality, a measure of communication between disease genes and differentially expressed genes. We find mediating pathways for three pulmonary diseases (asthma; bronchopulmonary dysplasia (BPD); and chronic obstructive pulmonary disease (COPD)) using pathway centrality. Mediating pathways shared by all three pulmonary disorders heavily favor inflammatory or immune responses and include specific pathways such as cytokine production, NF Kappa B, and JAK/STAT signaling. Disease-specific mediators, such as insulin signaling in BPD or homeostasis in COPD, are also highlighted. We support our findings, some of which suggest new treatment approaches, both with anecdotal evidence from the literature and via systematic evaluation using genetic interactions.peer-reviewed)

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Section: Methods and Resourcesmentioning

confidence: 99%

Pathway centrality in protein interaction networks identifies functional mediators of pulmonary disease

Park

Hescott

Slonim

2017

Preprint

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“…Decay dynamics also raised some computational aspects of the decay dynamics problem. Bhawalkar et al [29] and Zhang et al [30] provided a theoretical model and mathematical framework for finding the set of nodes whose deletion generates the smallest k-core subgraph of a network, focusing on the computational challenge of the decay. Their works assure that the node removal problem is relevant in social and other networks.…”

Section: Related Workmentioning

confidence: 99%

Postmortem Analysis of Decayed Online Social Communities: Cascade Pattern Analysis and Prediction

Abufouda

2018

Complexity

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Recently, many online social networks, such as MySpace, Orkut, and Friendster, have faced inactivity decay of their members, which contributed to the collapse of these networks. The reasons, mechanics, and prevention mechanisms of such inactivity decay are not fully understood. In this work, we analyze decayed and alive subwebsites from the Stack Exchange platform. The analysis mainly focuses on the inactivity cascades that occur among the members of these communities. We provide measures to understand the decay process and statistical analysis to extract the patterns that accompany the inactivity decay. Additionally, we predict cascade size and cascade virality using machine learning. The results of this work include a statistically significant difference of the decay patterns between the decayed and the alive subwebsites. These patterns are mainly cascade size, cascade virality, cascade duration, and cascade similarity. Additionally, the contributed prediction framework showed satisfactorily prediction results compared to a baseline predictor. Supported by empirical evidence, the main findings of this work are (1) there are significantly different decay patterns in the alive and the decayed subwebsites of the Stack Exchange; (2) the cascade's node degrees contribute more to the decay process than the cascade's virality, which indicates that the expert members of the Stack Exchange subwebsites were mainly responsible for the activity or inactivity of the Stack Exchange subwebsites; (3) the Statistics subwebsite is going through decay dynamics that may lead to it becoming fully-decayed; (4) the decay process is not governed by only one network measure, it is better described using multiple measures; (5) decayed subwebsites were originally less resilient to inactivity decay, unlike the alive subwebsites; and (6) network's structure in the early stages of its evolution dictates the activity/inactivity characteristics of the network.

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“…If a suitably sized stash can be implemented, peeling can efficiently find an assignment, leading to the question of how many edges need to be removed so the remaining hypergraph is k-peelable. 1 Even without such algorithmic implications, the minimum number of vertices or edges to remove to obtain a k-peelable graph appears a natural and interesting graph theoretic question.…”

Section: Introductionmentioning

confidence: 99%

“…We note that a similar problem was recently considered in [1]. In their variation, they look at the anchoring problem: given a budget b, find the subset B of b vertices such that peeling the graph of vertices from V − B of degree less than k yields the maximum number of remaining edges.…”

Section: Introductionmentioning

confidence: 99%

Hardness of peeling with stashes

Mitzenmacher

Nathan

2016

Information Processing Letters

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The analysis of several algorithms and data structures can be framed as a peeling process on a random graph: vertices with degree less than k and their adjacent edges are removed until no vertices of degree less than k are left. Often the question is whether the remaining graph, the k-core, is empty or not. In some settings, it may be possible to remove either vertices or edges from the graph before peeling, at some cost. For example, in hashing applications where keys correspond to edges and buckets to vertices, one might use an additional side data structure, commonly referred to as a stash, to separately handle some keys in order to avoid collisions. The natural question in such cases is to find the minimum number of edges (or vertices) that need to be stashed in order to realize an empty k-core.We show that both these problems are NP-complete for all k ≥ 2, with the sole exception being that the edge variant of stashing is solvable in polynomial time for k = 2 on standard (2-uniform) graphs.

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Preventing Unraveling in Social Networks: The Anchored k-Core Problem

Cited by 23 publications

References 14 publications

Pathway centrality in protein interaction networks identifies functional mediators of pulmonary disease

Pathway centrality in protein interaction networks identifies functional mediators of pulmonary disease

Postmortem Analysis of Decayed Online Social Communities: Cascade Pattern Analysis and Prediction

Hardness of peeling with stashes

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