Analysis of Network Clustering Algorithms and Cluster Quality Metrics at Scale

Notions of community quality underlie network clustering. While studies surrounding network clustering are increasingly common, a precise understanding of the realtionship between different cluster quality metrics is unknown. In this paper, we examine the relationship between stand-alone cluster quality metrics and information recovery metrics through a rigorous analysis of four widely-used network clustering algorithms -- Louvain, Infomap, label propagation, and smart local moving. We consider the stand-alone quality metrics of modularity, conductance, and coverage, and we consider the information recovery metrics of adjusted Rand score, normalized mutual information, and a variant of normalized mutual information used in previous work. Our study includes both synthetic graphs and empirical data sets of sizes varying from 1,000 to 1,000,000 nodes. We find significant differences among the results of the different cluster quality metrics. For example, clustering algorithms can return a value of 0.4 out of 1 on modularity but score 0 out of 1 on information recovery. We find conductance, though imperfect, to be the stand-alone quality metric that best indicates performance on information recovery metrics. Our study shows that the variant of normalized mutual information used in previous work cannot be assumed to differ only slightly from traditional normalized mutual information. Smart local moving is the best performing algorithm in our study, but discrepancies between cluster evaluation metrics prevent us from declaring it absolutely superior. Louvain performed better than Infomap in nearly all the tests in our study, contradicting the results of previous work in which Infomap was superior to Louvain. We find that although label propagation performs poorly when clusters are less clearly defined, it scales efficiently and accurately to large graphs with well-defined clusters

Defining and Evaluating Network Communities based on Ground-truth

Nodes in real-world networks organize into densely linked communities where edges appear with high concentration among the members of the community. Identifying such communities of nodes has proven to be a challenging task mainly due to a plethora of definitions of a community, intractability of algorithms, issues with evaluation and the lack of a reliable gold-standard ground-truth. In this paper we study a set of 230 large real-world social, collaboration and information networks where nodes explicitly state their group memberships. For example, in social networks nodes explicitly join various interest based social groups. We use such groups to define a reliable and robust notion of ground-truth communities. We then propose a methodology which allows us to compare and quantitatively evaluate how different structural definitions of network communities correspond to ground-truth communities. We choose 13 commonly used structural definitions of network communities and examine their sensitivity, robustness and performance in identifying the ground-truth. We show that the 13 structural definitions are heavily correlated and naturally group into four classes. We find that two of these definitions, Conductance and Triad-participation-ratio, consistently give the best performance in identifying ground-truth communities. We also investigate a task of detecting communities given a single seed node. We extend the local spectral clustering algorithm into a heuristic parameter-free community detection method that easily scales to networks with more than hundred million nodes. The proposed method achieves 30% relative improvement over current local clustering methods.Comment: Proceedings of 2012 IEEE International Conference on Data Mining (ICDM), 201

Node-Centric Detection of Overlapping Communities in Social Networks

We present NECTAR, a community detection algorithm that generalizes Louvain method's local search heuristic for overlapping community structures. NECTAR chooses dynamically which objective function to optimize based on the network on which it is invoked. Our experimental evaluation on both synthetic benchmark graphs and real-world networks, based on ground-truth communities, shows that NECTAR provides excellent results as compared with state of the art community detection algorithms

IMPACT: Investigation of Mobile-user Patterns Across University Campuses using WLAN Trace Analysis

We conduct the most comprehensive study of WLAN traces to date. Measurements collected from four major university campuses are analyzed with the aim of developing fundamental understanding of realistic user behavior in wireless networks. Both individual user and inter-node (group) behaviors are investigated and two classes of metrics are devised to capture the underlying structure of such behaviors. For individual user behavior we observe distinct patterns in which most users are 'on' for a small fraction of the time, the number of access points visited is very small and the overall on-line user mobility is quite low. We clearly identify categories of heavy and light users. In general, users exhibit high degree of similarity over days and weeks. For group behavior, we define metrics for encounter patterns and friendship. Surprisingly, we find that a user, on average, encounters less than 6% of the network user population within a month, and that encounter and friendship relations are highly asymmetric. We establish that number of encounters follows a biPareto distribution, while friendship indexes follow an exponential distribution. We capture the encounter graph using a small world model, the characteristics of which reach steady state after only one day. We hope for our study to have a great impact on realistic modeling of network usage and mobility patterns in wireless networks.Comment: 16 pages, 31 figure

Put three and three together: Triangle-driven community detection

Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its applications in many fields such as biology, social networks, or network traffic analysis. Although the existing metrics used to quantify the quality of a community work well in general, under some circumstances, they fail at correctly capturing such notion. The main reason is that these metrics consider the internal community edges as a set, but ignore how these actually connect the vertices of the community. We propose the Weighted Community Clustering (WCC), which is a new community metric that takes the triangle instead of the edge as the minimal structural motif indicating the presence of a strong relation in a graph. We theoretically analyse WCC in depth and formally prove, by means of a set of properties, that the maximization of WCC guarantees communities with cohesion and structure. In addition, we propose Scalable Community Detection (SCD), a community detection algorithm based on WCC, which is designed to be fast and scalable on SMP machines, showing experimentally that WCC correctly captures the concept of community in social networks using real datasets. Finally, using ground-truth data, we show that SCD provides better quality than the best disjoint community detection algorithms of the state of the art while performing faster.Peer ReviewedPostprint (author's final draft

Considerations about multistep community detection

The problem and implications of community detection in networks have raised a huge attention, for its important applications in both natural and social sciences. A number of algorithms has been developed to solve this problem, addressing either speed optimization or the quality of the partitions calculated. In this paper we propose a multi-step procedure bridging the fastest, but less accurate algorithms (coarse clustering), with the slowest, most effective ones (refinement). By adopting heuristic ranking of the nodes, and classifying a fraction of them as `critical', a refinement step can be restricted to this subset of the network, thus saving computational time. Preliminary numerical results are discussed, showing improvement of the final partition.Comment: 12 page