Related papers: Modularity bounds for clusters located by leading …
We prove that a class of graphs with an excluded minor and with the maximum degree sublinear in the number of edges is maximally modular, that is, modularity tends to 1 as the number of edges tends to infinity.
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
We consider families of mappings with moduli inequalities, having different definition domains. Under some additional assumptions we have proved that such families are uniformly equicontinuous. We have considered four main cases: when…
In July 2012, at the Conference on Applications of Graph Spectra in Computer Science, Barcelona, D. Stevanovic posed the following open problem: which graphs have the zero as the largest eigenvalue of their modularity matrix? The conjecture…
An old idea in optimization theory says that since the gradient is a dual vector it may not be subtracted from the weights without first being mapped to the primal space where the weights reside. We take this idea seriously in this paper…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the…
The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural…
We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph…
We initiate a study of Hilbert modules over the polynomial algebra A=C[z_1,...,z_d] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity…
The modular structure of brain networks supports specialized information processing, complex dynamics, and cost-efficient spatial embedding. Inter-individual variation in modular structure has been linked to differences in performance,…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…
Strong inter-dependence in complex systems can manifest as partially bipartite networks characterized by interactions occurring primarily between distinct groups of nodes (identified as modules). In this paper, we show that the anti-modular…
Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success.…
For a given graph $G$, each partition of the vertices has a modularity score, with higher values indicating that the partition better captures community structure in $G$. The modularity $q^*(G)$ of the graph $G$ is defined to be the maximum…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…