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The authors of \cite{Miller} propose the use of detection and estimation theory as defined for vector spaces with Gaussian noise in the context of graph analytics framework creating a new research area at the intersection of this domains. It is applied in the situational awareness cyber security to detect suspicious activity. Small subsets of vertices whose interactions do not fit the typical behaviour are identified. Relationships modeled as a graph are dificult to be analized in the Detection Theory framework. Translation and scaling are difficult to define for combinatorial and discrete graphs.  \cite{Sandryhaila}  \subsection{Social Networks}  \cite{Sizov_2010} studies authority ranking on social networks. The use of hashtags are indicative of emergent semantics in modern social networks as in \cite{Dellschaft_2009}. The authors formaly define social graphs and the application of tensors for authority ranking. A SocialWeb graph is defined as a graph G = ( V, L, E, linkType ) where V is the set of users in the community, L is the set of literals (e.g., hashtags), and E is the set of relations between users in V . Additionally, the function linkType : E -> L returns the annotation from L that relates two users. User X links to user Y by edge of type Z iff a) X follows Y (in the common sense of Twitter) and b) both X and Y have recently used the hashtag Z in their own postings/tweets. The authors describe the data collection and transformation processes for Twitter. 
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\cite{Guille_2013} information diffusion  \subsection{Information \subsection{Spectral Information  Retrieval} \cite{Costa_2010} describes how the Discret Fourier Transform (DFT) can be used for Information Retrieval (IR). A query is represented as a sum of individual query terms represented as sinusoidal curves. The query function is transformed in the frequency domain through DFT resulting a spectrum. Each document is considered to be a set of filters that filter the query spectrum resulting a power that ranks the documents. The more the power of the spectrum is decreased the higher the document ranks. The model is named Least Spectral Power Ranking (LSPR). The model can be used for recommender systems.  \cite{Ramamohanarao_2004} is an earlier spectral based method for IR. Apart from term frequencies it uses the term position in the documents. documents represented as the phase of the signal.  "It calculates document scores based on the query term spectra derived from query term signals." To handle signal shifts the Fourier transform is used. \cite{Caputo_2009}