The Routing of Complex Contagion in Kleinberg's Small-World Networks

  title={The Routing of Complex Contagion in Kleinberg's Small-World Networks},
  author={Wei Chen and Qiang Li and Xiaoming Sun and Jialin Zhang},
In Kleinberg's small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node $u$ with node $v$ through a weak tie is proportional to $1/|uv|^\alpha$, where $|uv|$ is the grid distance between $u$ and $v$ and $\alpha\ge 0$ is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only… 

Influence Maximization with ε-Almost Submodular Threshold Functions

This paper explores influence maximization in the nonsubmodular regime with a general threshold model in which a fraction of nodes have non-submodular threshold functions, but their threshold functions are closely upperand lower-bounded by some submodular functions.



Complex Contagions in Kleinberg's Small World Model

Two subtly different variants of Kleinberg's small world model are studied and it is shown that there is an intermediate range of values, such that when γ takes any of these values, a k-complex contagion spreads quickly on the corresponding graph, in a polylogarithmic number of rounds.

Complex contagion and the weakness of long ties in social networks: revisited

Three small world models are studied and rigorous analysis on the diffusion speed of a k-complex contagion, in which a node becomes active only when at least k of its neighbors are active, showing that compared to simple contagions, weak ties are not as effective in spreading complex contagions due to the lack of simultaneous active contacts.

On the searchability of small-world networks with arbitrary underlying structure

It is shown that for a simple long-range contact distribution consistent with empirical observations on social networks, a slight variation of greedy search, where the next hop is to a distant node only if it yields sufficient progress towards the target, requires no(1) steps.

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On the approximability of influence in social networks

  • Ning Chen
  • Computer Science, Mathematics
    SODA '08
  • 2008
The main result says that the problem of minimizing the size of S, while ensuring that targeting S would influence the whole network into adopting the product, is hard to approximate within a polylogarithmic factor.

Scaling and percolation in the small-world network model.

  • M. NewmanD. Watts
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
There is one nontrivial length-scale in the small-world network model of Watts and Strogatz, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit.

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An analysis framework based on submodular functions shows that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models, and suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.

Bootstrap Percolation on Infinite Trees and Non-Amenable Groups

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Collective dynamics of ‘small-world’ networks

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Networks, Crowds, and Markets: Reasoning about a Highly Connected World

Over the past decade there has been a growing public fascination with the complex connectedness of modern society. This connectedness is found in many incarnations: in the rapid growth of the