Finding community structure in very large networks.
TLDR
A hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure.Abstract:
The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m approximately n and d approximately log n, in which case our algorithm runs in essentially linear time, O (n log(2) n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on-line retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 x 10(6) edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.read more
Citations
More filters
Journal ArticleDOI
Performance of modularity maximization in practical contexts
Benjamin H. Good,Benjamin H. Good,Yves-Alexandre de Montjoye,Yves-Alexandre de Montjoye,Aaron Clauset +4 more
TL;DR: It is shown that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum, implying that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts.
Journal ArticleDOI
Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities.
TL;DR: The basic ideas behind the previous benchmark are extended to generate directed and weighted networks with built-in community structure, and the possibility that nodes belong to more communities is considered, a feature occurring in real systems, such as social networks.
Posted Content
Empirical Comparison of Algorithms for Network Community Detection
TL;DR: In this paper, the authors explore a range of network community detection methods in order to compare them and to understand their relative performance and the systematic biases in the clusters they identify, and examine several different classes of approximation algorithms that aim to optimize such objective functions.
Proceedings ArticleDOI
Empirical comparison of algorithms for network community detection
TL;DR: Considering community quality as a function of its size provides a much finer lens with which to examine community detection algorithms, since objective functions and approximation algorithms often have non-obvious size-dependent behavior.
Posted Content
Communities in Networks
TL;DR: A survey of the concepts, methods, and applications of community detection can be found in this paper, where the authors provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems.
References
More filters
Journal ArticleDOI
Collective dynamics of small-world networks
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Journal ArticleDOI
Statistical mechanics of complex networks
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Journal ArticleDOI
The Structure and Function of Complex Networks
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.