Related papers: Modularity and random graphs
Community detection refers to finding densely connected groups of nodes in graphs. In important applications, such as cluster analysis and network modelling, the graph is sparse but outliers and heavy-tailed noise may obscure its structure.…
With invaluable theoretical and practical benefits, the problem of partitioning networks for community structures has attracted significant research attention in scientific and engineering disciplines. In literature, Newman's modularity…
Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…
There are good arguments to support the claim that deep neural networks (DNNs) capture better feature representations than the previous hand-crafted feature engineering, which leads to a significant performance improvement. In this paper,…
A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree.…
Community detection in networks is one of the most popular topics of modern network science. Communities, or clusters, are usually groups of vertices having higher probability of being connected to each other than to members of other…
Community-aware centrality is an emerging research area in network science concerned with the importance of nodes in relation to community structure. Measures are a function of a network's structure and a given partition. Previous…
We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural…
Communities are of great importance for understanding graph structures in social networks. Some existing community detection algorithms use a single prototype to represent each group. In real applications, this may not adequately model the…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…
The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to…
Community or modular structure is considered to be a significant property of large scale real-world graphs such as social or information networks. Detecting influential clusters or communities in these graphs is a problem of considerable…
Network community detection often relies on optimizing partition quality functions, like modularity. This optimization appears to be a complex problem traditionally relying on discrete heuristics. And although the problem could be…
For a graph class $\mathcal{G}$, we define the $\mathcal{G}$-modular cardinality of a graph $G$ as the minimum size of a vertex partition of $G$ into modules that each induces a graph in $\mathcal{G}$. This generalizes other module-based…
Graph theoretical analysis of the community structure of networks attempts to identify the communities (or modules) to which each node affiliates. However, this is in most cases an ill-posed problem, as the affiliation of a node to a single…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
We prove asymptotically optimal bounds on the number of edges a graph $G$ must have in order that any $r$-colouring of $E(G)$ has a colour class which contains every $D$-degenerate graph on $n$ vertices with bounded maximum degree. We also…
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e. random graphs…
We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We…