A Network Formation Model Based on Subgraphs

@article{Chandrasekhar2016ANF,
  title={A Network Formation Model Based on Subgraphs},
  author={Arun Chandrasekhar and Matthew O. Jackson},
  journal={Demand \& Supply in Health Economics eJournal},
  year={2016}
}
We develop a new class of random-graph models for the statistical estimation of network formation that allow for substantial correlation in links. Various subgraphs (e.g., links, triangles, cliques, stars) are generated and their union results in a network. The challenge in estimating the frequencies with which subgraphs 'truly' form is that subgraphs can overlap and may also incidentally generate new subgraphs, and so the true rate of formation of the subgraphs cannot generally be inferred… 

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References

SHOWING 1-10 OF 101 REFERENCES

Tractable and Consistent Random Graph Models

This work provides the first general results on when these models' parameters estimated from the observation of a single network are consistent (i.e., become accurate as the number of nodes grows), and shows how choice-based (strategic) network formation models can be written as SERGMs and SUGMs, and apply the models and techniques to network data from rural Indian villages.

A Structural Model of Dense Network Formation

  • A. Mele
  • Computer Science, Mathematics
  • 2017
An empirical model of network formation, combining strategic and random networks features, and provides new identification results for ERGMs in large networks: if link externalities are nonnegative, the ERGM is asymptotically indistinguishable from an Erdős–Renyi model with independent links.

CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.

It is shown that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power.

Mixing Time of Exponential Random Graphs

In the high temperature regime, where sampling with MCMC is possible, it is shown that any finite collection of edges are asymptotically independent; thus, the model does not possess the desired reciprocity property, and is not appreciably different from the Erdos-Renyi random graph.

Identi…cation and Estimation of Network Formation Games

Social and economic networks play an important role in shaping individual behaviors. In this paper, we aim to identify and estimate network formation games using observed data on network structure,

Meeting Strangers and Friends of Friends: How Random are Social Networks?

It is shown that as the random/network-based meeting ratio varies, the resulting degree distributions can be ordered in the sense of stochastic dominance, which allows us to infer how the formation process affects average utility in the network.

Identification of Preferences in Network Formation Games

A framework for identifying preferences in a large network under the assumption of pairwise stability of network links is provided and a quadratic programming algorithm is provided that can be used to construct the identified sets.

Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp

A large class of models, including several generalizations of stochastic block models, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies are described and extended.

Random graphs with a given degree sequence

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is

Statistical mechanics of networks.

  • Juyong ParkM. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of
...