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

@article{Chen2016TheRO,
title={The Routing of Complex Contagion in Kleinberg's Small-World Networks},
author={Wei Chen and Qiang Li and Xiaoming Sun and Jialin Zhang},
journal={ArXiv},
year={2016},
volume={abs/1503.00448}
}
• Wei Chen
• Published 2 March 2015
• Computer Science
• ArXiv
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…
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## References

SHOWING 1-10 OF 28 REFERENCES

### Complex Contagions in Kleinberg's Small World Model

• Mathematics
ITCS
• 2015
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

• Computer Science
EC '13
• 2013
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

• Computer Science
STOC '10
• 2010
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.

### The effect of power-law degrees on the navigability of small worlds: [extended abstract]

• Computer Science
PODC '09
• 2009
These results are the first to formally quantify the effect of the power-law degree distribution on the navigability of small worlds, and show that this effect is significant.

### 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.

• 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.

### Maximizing the spread of influence through a social network

• Computer Science
KDD '03
• 2003
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

• Mathematics
Combinatorics, Probability and Computing
• 2006
It is proved that on any $2k-regular non-amenable graph, the critical probability for the$k$-rule is strictly positive, and that in any rooted tree$T\$ there is a way of erasing children of the root, together with all their descendants, and repeating this for all remaining children, and so on.

### Collective dynamics of ‘small-world’ networks

• Computer Science
Nature
• 1998
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.

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

• Economics
• 2010
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