Abstract. Due to nowadays networks' sizes, the evaluation of a community detection algorithm can only be done using quality functions. These functions measure different networks/graphs structural properties, each of them corresponding to a different definition of a community. Since there exists many definitions for a community, choosing a quality function may be a difficult task, even if the networks' statistics/origins can give some clues about which one to choose. In this paper, we apply a general methodology to identify different contexts, i.e. groups of graphs where the quality functions behave similarly. In these contexts we identify the best quality functions, i.e. quality functions whose results are consistent with expectations from real life applications.
10 pages, 8 figuresInternational audienceThis article presents an efficient hierarchical clustering algorithm that solves the problem of core community detection. It is a variant of the standard community detection problem in which we are particularly interested in the connected core of communities. To provide a solution to this problem, we question standard definitions on communities and provide alternatives. We also propose a function called compactness, designed to assess the quality of a solution to this problem. Our algorithm is based on a graph traversal algorithm, the LexDFS. The time complexity of our method is in $O(n\times log(n))$. Experiments show that our algorithm creates highly compact clusters
This paper provides a probabilistic analysis of an algorithm which computes the gcd of inputs (with ≥ 2), with a succession of − 1 phases, each of them being the Euclid algorithm on two entries. This algorithm is both basic and natural, and two kinds of inputs are studied: polynomials over the finite field Fq and integers. The analysis exhibits the precise probabilistic behaviour of the main parameters, namely the number of iterations in each phase and the evolution of the length of the current gcd along the execution. We first provide an average-case analysis. Then we make it even more precise by a distributional analysis. Our results rigorously exhibit two phenomena: (i) there is a strong difference between the first phase, where most of the computations are done and the remaining phases; (ii) there is a strong similarity between the polynomial and integer cases.
Abstract. The analysis of dynamic networks has received a lot of attention in recent years, thanks to the greater availability of suitable datasets. One way to analyse such dataset is to study temporal motifs in link streams , i.e. sequences of links for which we can assume causality. In this article, we study the relationship between temporal motifs and communities, another important topic of complex networks. Through experiments on several real-world networks, with synthetic and ground truth community partitions, we identify motifs that are overrepresented at the frontier -or inside of-communities.
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