Rumors in a Network: Who's the Culprit?

@article{Shah2011RumorsIA,
  title={Rumors in a Network: Who's the Culprit?},
  author={Devavrat Shah and Tauhid Zaman},
  journal={IEEE Transactions on Information Theory},
  year={2011},
  volume={57},
  pages={5163-5181}
}
  • D. Shah, Tauhid Zaman
  • Published 24 September 2009
  • Computer Science
  • IEEE Transactions on Information Theory
We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with the popular susceptible-infected (SI) model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term rumor centrality. We establish that this is a maximum likelihood (ML) estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a… 

Figures from this paper

Finding Rumor Sources on Random Graphs
We consider the problem of detecting the source of a rumor (information diffusion) in a network based on observations about which set of nodes posses the rumor. In a recent work [10] by the authors,
Fast rumor source identification via random walks
TLDR
This work proposes a heuristic based on the hitting time statistics of a surrogate random walk process that can be used to approximate the maximum likelihood estimator of the rumor source.
Rumor spreading maximization and source identification in a social network
  • Wuqiong Luo, Wee Peng Tay, M. Leng
  • Computer Science
    2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM)
  • 2015
TLDR
Simulations in both synthetic and real-world networks demonstrate that the proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.
Estimating the Origin of Diffusion in Complex Networks with Limited Observations
TLDR
This work presents an algorithm which utilizes the correlated information between the network structure (shortest paths) and the diffusion dynamics (time sequence of infection) and shows that it leads to significant improvement of performance compared to existing approaches.
An Algorithmic Framework for Estimating Rumor Sources With Different Start Times
TLDR
This work introduces the concepts of a quasi-regular tree and a heavy center, which allows for an algorithmic framework that transforms an abstract estimator into a two-source joint estimator, in which the infection graph can be thought of as covered by overlapping infection regions.
Rooting our Rumor Sources in Online Social Networks: The Value of Diversity From Multiple Observations
TLDR
Surprisingly, even with merely two observations, the detection probability at least doubles that of a single observation, and further approaches one, i.e., reliable detection, with increasing degree, indicating that a richer diversity enhances detectability.
Identifying source of an information in complex networks with limited observation nodes
TLDR
This work studies the problem of estimating the origin of a rumor/epidemic outbreak: given a contact network and a snapshot of epidemic spread at a certain time, determine the infection source and introduces an inference algorithm based on sparsely placed observers.
Locating the epidemic source in complex networks
TLDR
The problem of estimating the origin of a disease/rumor outbreak is studied: given a contact network and a snapshot of epidemic spread at a certain time, root out the infection source and introduce an inference algorithm based on sparsely placed observers.
Rumor Spreading and Source Identification: A Hide and Seek Game
TLDR
Simulations in both synthetic and real-world networks demonstrate that the proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.
Rumor source detection under probabilistic sampling
TLDR
This work provides the extension to the case in which nodes reveal whether they have heard the rumor with probability p, independent of each other, and achieves the same performance as the optimal estimator with p = 1.
...
...

References

SHOWING 1-10 OF 40 REFERENCES
The effect of network topology on the spread of epidemics
  • A. Ganesh, L. Massoulié, D. Towsley
  • Mathematics, Computer Science
    Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies.
  • 2005
TLDR
This paper identifies topological properties of the graph that determine the persistence of epidemics and shows that if the ratio of cure to infection rates is larger than the spectral radius of thegraph, then the mean epidemic lifetime is of order log n, where n is the number of nodes.
Spread of epidemic disease on networks.
  • M. Newman
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
TLDR
This paper shows that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks.
Epidemic spreading in scale-free networks.
TLDR
A dynamical model for the spreading of infections on scale-free networks is defined, finding the absence of an epidemic threshold and its associated critical behavior and this new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.
Collective dynamics of ‘small-world’ networks
TLDR
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Epidemics and percolation in small-world networks.
  • C. Moore, M. Newman
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
TLDR
The resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network, and are given exact solutions for the position of this threshold in a variety of cases.
Reconstruction on Trees: Beating the Second Eigenvalue
TLDR
It is shown that, both for the binary asymmetric channel and for the symmetric channel on many symbols, it is sometimes possible to reconstruct even when dλ22(M) < 1, indicating that, for many (maybe most) tree-indexed Markov chains, the location of the data on the boundary plays a crucial role in reconstruction problems.
Emergence of scaling in random networks
TLDR
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
First-Passage Percolation
First-passage percolation was introduced by Hammersley and Welsh in 1965 (see [13]), partly as a generalization of ordinary percolation. (For later surveys see [36], [21] and [22].) It can be thought
Generating random spanning trees
  • A. Broder
  • Computer Science, Mathematics
    30th Annual Symposium on Foundations of Computer Science
  • 1989
TLDR
It is shown that the Markov chain on the space of all spanning trees of a given graph where the basic step is an edge swap is rapidly mixing.
Bayesian inference for stochastic multitype epidemics in structured populations via random graphs
Summary.  The paper is concerned with new methodology for statistical inference for final outcome infectious disease data using certain structured population stochastic epidemic models. A major
...
...