Degree relations of triangles in real-world networks and graph models

  title={Degree relations of triangles in real-world networks and graph models},
  author={Nurcan Durak and Ali Pinar and Tamara G. Kolda and Seshadhri Comandur},
  journal={Proceedings of the 21st ACM international conference on Information and knowledge management},
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… 

Figures and Tables from this paper

Counting Triangles in Massive Graphs with MapReduce

This paper describes how to implement a recent wedge-sampling algorithm in MapReduce to deal with massive graphs, and shows results on publicly available networks, as well as artificially generated networks.

Directed Random Geometric Graphs

The DRGG model is introduced, which is an extension of the random geometric graph model, and it is proved that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, and has a high clustering coefficient, has few edges and is likely small-world.

Using Triangles to Improve Community Detection in Directed Networks

This work proposes an undirected edge-weighting scheme based on directed trian- gles that improves a task where plausible ground-truth communities are known and proposes a new metric on quality of communities that is based on the number of 3-cycles that are split across communities.

The impossibility of low-rank representations for triangle-rich complex networks

It is mathematically proved that low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, and any embedding that can successfully create these two properties must have a rank that is nearly linear in the number of vertices.

Triadic Measures on Graphs: The Power of Wedge Sampling

This work proposes a new method based on wedge sampling that allows for the fast and accurate approximation of all current variants of clustering coefficients and enables rapid uniform sampling of the triangles of a graph.

Wedge sampling for computing clustering coefficients and triangle counts on large graphs †

This work considers wedge sampling, which provides faster and more accurate approximations than competing techniques, and provides extensive results that show its methods are both more accurate and faster than state‐of‐the‐art alternatives.

Self-Coordinated Corona Graphs: a model for complex networks

A deterministic complex network model, which is called Self-Coordinated Corona Graphs (SCCG), based on the corona product of graphs, where the networks in the proposed model are generated by the virtue of self coordination of nodes in corona graphs.

Evolution of Directed Triangle Motifs in the Google+ OSN

It is found that users in more symmetric triangle motifs live closer together, indicating more personal relationships, and that many triangles evolve into less-connected motifs (with less edges), suggesting that growth also comes with pruning.

A Note on Detection of Communities in Social Networks

  • P. Sridevi
  • Computer Science
    International Journal of Engineering and Computer Science
  • 2020
This work takes into consideration, a triangle instead of the edge as the basic indicator of a strong relation in the social graph and uses it to detect strong communities in a Social Network.

Mining statistically significant connected subgraphs in vertex labeled graphs

This paper addresses the problem of finding statistically significant connected subgraphs where the nodes of the graph are labeled by introducing the notion of contracting edges that merge vertices together to form a super-graph and using the chi-square statistic as a measure for quantifying the statistical significance.



Fast Counting of Triangles in Large Real Networks without Counting: Algorithms and Laws

Two new power laws (degree-triangle and triangleparticipation laws) with surprising properties are discovered, and the eigentrianglelocal algorithm that gives the count of triangles that contain a desired node is provided.

Community structure and scale-free collections of Erdös-Rényi graphs

The Block Two-Level Erdős-Rényi (BTER) model is proposed, and it is demonstrated that it accurately captures the observable properties of many real-world social networks.

Efficient semi-streaming algorithms for local triangle counting in massive graphs

This is the first paper that addresses the problem of local triangle counting with a focus on the efficiency issues arising in massive graphs and proposes two approximation algorithms, which are based on the idea of min-wise independent permutations.

Graphs over time: densification laws, shrinking diameters and possible explanations

A new graph generator is provided, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.

The Web as a Graph: Measurements, Models, and Methods

This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet.

Are technological and social networks really different

It is said that the most minimal network structural constraint, D, can explain observed r<0 but that network circumstances and context are necessary to explain observedrτ;0.

Neighborhoods are good communities

It is theoretically demonstrate that two commonly observed properties of social networks, heavy-tailed degree distributions and large clustering coefficients, imply the existence of vertex neighborhoods (also known as egonets) that are themselves good communities.

Systematic topology analysis and generation using degree correlations

This work presents a new, systematic approach for analyzing network topologies, introducing the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G, and demonstrates that these graphs reproduce, with increasing accuracy, important properties of measured and modeled Internet topologies.

Biological network comparison using graphlet degree distribution

Almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, as well as from curated databases, are better modeled by geometric random graphs than by Erdös-Rény, random scale-free, or Barabási-Albert scale- free networks.

Exploring the assortativity-clustering space of a network's degree sequence.

  • P. HolmeJ. Zhao
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
This work argues that this ensemble of graphs with the same set of degrees can give more information about the original network than effective values of network structural quantities, and finds that high clustering might be a force in the evolution of protein interaction networks.