Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Testing the diameter of graphs
Random Structures & Algorithms
Tight Bounds for Testing Bipartiteness in General Graphs
SIAM Journal on Computing
Testing triangle-freeness in general graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
An Expansion Tester for Bounded Degree Graphs
SIAM Journal on Computing
Hi-index | 0.00 |
In the new century, the study of networks is being developed rapidly. Traditional algorithms based on the classical graph theory have not been able to cope with large scaled networks due to their inefficiency. In this paper, we review the research on the question why a huge network such as the www-network is efficiently computable, and investigate the principles of network computing. Networks cannot be fully and exactly computed due to both their nature and their scales. The best possibility of network computing could be just locally testable graph properties, in sparse graph models. We review the progress of the study of graph property test, in particular, local test of conductance of graphs, which is closely related to the basic network structural cells --- small communities. In the past decade, an avalanche of research has shown that many real networks, independent of their age, function, and scope, converge to similar architectures, which is probably the most surprising discovery of modern network theory. In many ways, there is a need to understand the dynamics of the processes that take place in networks. We propose a new local mechanism by introducing one more dimension for each node in a network and define a new model of networks, the homophily model, from which we are able to prove the homophily theorem that implies the homophily law of networks. The homophily law ensures that real world networks satisfies the small community phenomenon, and that nodes within a small community share some remarkable common features.