Finding community structure in very large networks

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.

Structural vulnerability of the French swine industry trade network to the spread of infectious diseases

“…In principle, the maximum value of the modularity is Q max 5 1 and such a network could be considered as highly modular. Nevertheless, it is lower for most real networks (Good et al, 2010) and modularity can be considered to be high from 0.5 (Clauset et al, 2004). Here, the modularity tended to Figure 6 Spatial distribution of the largest communities (.1000 holdings) of the 6-month swine trade network including slaughterhouses, France, 2010; seven large communities in networks including slaughterhouses (right) and four large communities in networks excluding slaughterhouses (left).…”

“…We used the 'greedy algorithms' method proposed by Newman (Clauset et al, 2004;Newman, 2004), which can only be applied on one-mode networks. We, therefore, identified communities in the global one-mode network with and without movements to a slaughterhouse.…”

Checking the reliability of a linear-programming based approach towards detecting community structures in networks

“…[25]). Their approach was further improved by the "CNM algorithm" proposed by Clauset et al [8] who developed an extremely fast heuristic that greedily searches for modularity-optimal community structures, returns demonstrably good results for many real-world networks, and has often been used successfully in recent years (see, e.g., [35] for a recent biological application).…”

Bibliometric Analysis of Collaboration Network and the Role of Research Station in Antarctic Science

“…High modularity value indicates there exists a community structure in the network (Clauset et al, 2004;). Moreover, in order to examine the effect of research station, we calculate relative growth rate (RGR) and doubling time t D by using the number of papers that estimated from our collaboration network.…”

“…Maximum modularity value of the network is 0.587 that is larger than 0.3 which considered as a good indicator of community structure in a network (Clauset et al, 2004). In Table 2, detected communities and member countries are listed in descending order of community size.…”