Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Scalable modeling of real graphs using Kronecker multiplication
Proceedings of the 24th international conference on Machine learning
Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Graph Twiddling in a MapReduce World
Computing in Science and Engineering
Power-Law Distributions in Empirical Data
SIAM Review
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Measurement-calibrated graph models for social network experiments
Proceedings of the 19th international conference on World wide web
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Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what these triangles look like. We initiate the study of degree-labeled triangles, - specifically, degree homogeneity versus heterogeneity in triangles. This yields new insight into the structure of real-world graphs. We observe that networks coming from social and collaborative situations are dominated by homogeneous triangles, i.e., degrees of vertices in a triangle are quite similar to each other. On the other hand, information networks (e.g., web graphs) are dominated by heterogeneous triangles, i.e., the degrees in triangles are quite disparate. Surprisingly, nodes within the top 1% of degrees participate in the vast majority of triangles in heterogeneous graphs. We investigate whether current graph models reproduce the types of triangles that are observed in real data and observe that most models fail to accurately capture these salient features.