# Finding And Evaluating Community Structure In Networks Pdf

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*We propose and study a set of algorithms for discovering community structure in networks—natural divisions of network nodes into densely connected subgroups. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.*

- Performance Evaluation of Modularity Based Community Detection Algorithms in Large Scale Networks
- Community structure
- Completeness of Community Structure in Networks
- Completeness of Community Structure in Networks

## Performance Evaluation of Modularity Based Community Detection Algorithms in Large Scale Networks

Community structure detection is one of the major research areas of network science and it is particularly useful for large real networks applications. The computational complexity of the algorithms is analysed for the development of a high performance code to accelerate the execution of these algorithms without compromising the quality of the results, according to the modularity measure. The code was applied to a wide range of real networks and the performances of the algorithms are evaluated. Community detection is of great interest in the field of complex networks and its study has been subject of many works [ 1 — 6 ]. A consensual notion about the characterization of a community in a network is a subset of nodes with great internal density and low external density.

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. By defining a new measure to community structure, exclusive modularity , and based on cavity method of statistical physics, we develop a mathematically principled method to determine the completeness of community structure, which represents whether a partition that is either annotated by experts or given by a community-detection algorithm, carries complete information about community structure in the network. Our results demonstrate that the expert partition is surprisingly incomplete in some networks such as the famous political blogs network, indicating that the relation between meta-data and community structure in real-world networks needs to be re-examined.

We propose and study a set of algorithms for discovering community structure in networks—natural divisions of network nodes into densely connected subgroups. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems. Newman 1,2 and M. COVID has impacted many institutions and organizations around the world, disrupting the progress of research.

## Community structure

Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM Order Statistics Local Optimization Method , the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs.

In the study of complex networks , a network is said to have community structure if the nodes of the network can be easily grouped into potentially overlapping sets of nodes such that each set of nodes is densely connected internally. In the particular case of non-overlapping community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But overlapping communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community ies , and less likely to be connected if they do not share communities. A related but different problem is community search , where the goal is to find a community that a certain vertex belongs to. In the study of networks , such as computer and information networks, social networks and biological networks, a number of different characteristics have been found to occur commonly, including the small-world property , heavy-tailed degree distributions , and clustering , among others. Another common characteristic is community structure.

Download PDF. Abstract: We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of.

## Completeness of Community Structure in Networks

By defining a new measure to community structure, exclusive modularity , and based on cavity method of statistical physics, we develop a mathematically principled method to determine the completeness of community structure, which represents whether a partition that is either annotated by experts or given by a community-detection algorithm, carries complete information about community structure in the network. Our results demonstrate that the expert partition is surprisingly incomplete in some networks such as the famous political blogs network, indicating that the relation between meta-data and community structure in real-world networks needs to be re-examined. As a byproduct we find that the exclusive modularity, which introduces a null model based on the degree-corrected stochastic block model, is of independent interest. We discuss its applications as principled ways of detecting hidden structures, finding hierarchical structures without removing edges, and obtaining low-dimensional embedding of networks. Community structure, a partition of nodes into groups in such a way that the number of edges within groups is comparatively larger than the number of edges between groups, has attracted great attention over the past decade 1 — 3.

Radatools is a set of freely distributed programs to analyze Complex Networks. In particular, it includes programs for Communities Detection, Mesoscales Determination, calculation of Network Properties, and general tools for the manipulation of Networks and Partitions. There are also several programs not strictly related with networks, standing out one for Agglomerative Hierarchical Clustering using Multidendrograms and Binary Dendrograms. Radatools is just a set of binary executable programs whose source code is available in Radalib.

*Morris, David J.*

### Completeness of Community Structure in Networks

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