In a smart grid environment, we study coalition formation of prosumers that aim at entering the energy market. It is paramount for the grid operation that the energy producers are able to sustain the grid demand in terms of stability and minimum production requirement. We design an algorithm that seeks to form coalitions that will meet both of these requirements: a minimum energy level for the coalitions and a steady production level which leads to finding uncorrelated sources of energy to form a coalition. We propose an algorithm that uses graph tools such as correlation graphs or clique percolation to form coalitions that meet such complex constraints. We validate the algorithm against a random procedure and show that, it not only performs better in term of social welfare for the power grid, but also that it is more robust against unforeseen production variations due to changing weather conditions for instance.
Presented in this way, the time-series clustering task seems very close to graph community detection. Communities in networks are indeed often seen as groups of nodes exhibiting high internal densities of links as well as a low density across communities, and several topology oriented techniques for finding communities are present in the litterature ( @cite_12 @cite_13 @cite_18 ). For our purpose where decorrelation is the closeness notion, such algorithms tend to have some difficulties because only a few inclusions of very high correlations can strongly affect the stability of a coalition. However, local cliques, where all nodes are linked, provide uncorrelated groups of nodes. There exists greedy heuristics based on cliques in the litterature such as clique percolation @cite_17 which realizes local optimizations of a fitness function and results in overlaping community structures. Detection of overlapping communities is actually a very active field of research, especially in social networks where a person might belong to several communities.
@cite_18 @cite_13 @cite_12 @cite_17
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A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases. We consider three distinct and well-studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems can be tackled using spectral algorithms that make use of the eigenvectors of matrix representations of the network. We show that with certain choices of the free parameters appearing in these spectral algorithms the algorithms for all three problems are, in fact, identical, and hence that, at least within the spectral approximations used here, there is no difference between the modularity- and inference-based community detection methods, or between either and graph partitioning. Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here, we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling different hierarchical levels of organization to be investigated. Tests on real and artificial networks give excellent results.