Clique Community Research Articles

Beyond Topological Persistence: Starting from Networks

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and digraphs. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness—clique communities, k-vertex, and k-edge connectedness—directly on simple graphs and strong connectedness in digraphs.

<inline-formula> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula>-Clique Community Detection in Social Networks Based on Formal Concept Analysis

With the advent of ubiquitous sensing and networking, future social networks turn into cyber-physical interactions, which are attached with associated social attributes. Therefore, social network analysis is advancing the interconnections among cyber, physical, and social spaces. Community detection is an important issue in social network analysis. Users in a social network usually have some social interactions with their friends in a community because of their common interests or similar profiles. In this paper, an efficient algorithm of $k$ -clique community detection using formal concept analysis (FCA)—a typical computational intelligence technique, namely, FCA-based $k$ -clique community detection algorithm, is proposed. First, a formal context is constructed from a given social network by a modified adjacency matrix. Second, we define a type of special concept named $k$ -equiconcept, which has the same $k$ -size of extent and intent in a formal concept lattice. Then, we prove that the $k$ -clique detection problem is equivalent to finding the $k$ -equiconcepts. Finally, the efficient algorithms for detecting the $k$ -cliques and $k$ -clique communities are devised by virtue of $k$ -equiconcepts and $k$ -intent concepts, respectively. Experimental results demonstrate that the proposed algorithm has a higher $F$ -measure value and significantly reduces the computational cost compared with previous works. In addition, a correlation between $k$ and the number of $k$ -clique communities is investigated.

General clique percolation in random networks

A general clique community of a network, which consists of adjacent k-cliques sharing at least l vertices with , is introduced. With the emergence of a giant clique community in the network, there is a clique percolation. Using the largest size jump Δ of the largest clique community during network evolution and the corresponding evolution step Tc, we study the general clique percolation of the Erdős-Rényi network. We investigate the averages of Δ and Tc and their fluctuations for different network size N. The clique percolation can be identified by the power-law finite-size effects of the averages and root mean squares of fluctuation. The finite-size scaling distribution functions of fluctuations are calculated. The universality class of the clique percolation is characterized by the critical exponents of power-law finite-size effects. Using Monte Carlo simulations, we find that the Erdős-Rényi network experiences a series of clique percolation with . We find that the critical exponents and therefore the universality class of the clique percolation depend on clique connection index l, but are independent of clique size k.

지연 감내 네트워크에서 커뮤니티 기반 영향력 측정 기법

Influence propagation is an important research issue in social networks. Influence propagation means that the status or the disposition of nodes get changed by new idea, information and gossip propagated by other nodes. Influenced nodes also make other nodes influenced across the network. The influence propagation problem based on `word of mouth` referral is to find most influential nodes set in networks to maximize influence. In this paper, we study the influence measuring and finding most influential nodes set in Delay-Tolerant Networks. It is difficult to measure exact influential power in Delay-Tolerant networks where network topology is not stable due to the nodal mobility. In this paper, we propose a distributed scheme that each node constructs -clique community structure and estimates local influential power in Delay-Tolerant Networks. Simulation results show that the influential nodes information estimated by proposed scheme is in agreement with a global view of influential nodes information.

Sequential algorithm for fast clique percolation

In complex network research clique percolation, introduced by Palla, Derényi, and Vicsek [Nature (London) 435, 814 (2005)], is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network. Here we present a sequential clique percolation algorithm (SCP) to do fast community detection in weighted and unweighted networks, for cliques of a chosen size. This method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure. Unlike existing algorithms, the SCP method allows for detecting k -clique communities at multiple weight thresholds in a single run, and can simultaneously produce a dendrogram representation of hierarchical community structure. In sparse weighted networks, the SCP algorithm can also be used for implementing the weighted clique percolation method recently introduced by Farkas [New J. Phys. 9, 180 (2007)]. The computational time of the SCP algorithm scales linearly with the number of k -cliques in the network. As an example, the method is applied to a product association network, revealing its nested community structure.

Biclique communities

We present a method for detecting communities in bipartite networks. Based on an extension of the k -clique community detection algorithm, we demonstrate how modular structure in bipartite networks presents itself as overlapping bicliques. If bipartite information is available, the biclique community detection algorithm retains all of the advantages of the k -clique algorithm, but avoids discarding important structural information when performing a one-mode projection of the network. Further, the biclique community detection algorithm provides a level of flexibility by incorporating independent clique thresholds for each of the nonoverlapping node sets in the bipartite network.