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**1 - 5**of**5**### Feature Extraction from Degree Distribution for Comparison and Analysis of Complex Networks

, 2014

"... The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as xed-length feature vectors and therefore the feature extraction from the degree distribution is a necessary step. Moreover, many applications need a s ..."

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The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as xed-length feature vectors and therefore the feature extraction from the degree distribution is a necessary step. Moreover, many applications need a similarity function for comparison of complex networks based on their degree distributions. Such a similarity measure has many applications including classication and clustering of network instances, evaluation of network sampling methods, anomaly detection, and study of epidemic dynamics. The existing methods are unable to eectively capture the similarity of degree distributions, particularly when the corresponding networks have dierent sizes. In this paper, we propose a feature extraction method and a similarity function for the degree distributions in complex networks. We propose to calculate the feature values based on the mean and standard deviation of the node degrees in order to decrease the eect of the network size on the extracted features. Experiments on a wide range of real and articial networks conrms the accuracy, stability, and eectiveness of the proposed method.

### 2014 7th International Symposium on Telecommunications (IST’2014) Quantification and Comparison of Degree Distributions in Complex Networks

"... Abstract—The degree distribution is an important characteris-tic in complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. Additionally, we often need to compare the degree distribution of two given networks and ..."

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Abstract—The degree distribution is an important characteris-tic in complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. Additionally, we often need to compare the degree distribution of two given networks and extract the amount of similarity between the two distributions. In this paper, we propose a novel method for quantification of the degree distributions in complex networks. Based on this quantification method, a new distance function is also proposed for degree distributions, which captures the differences in the overall structure of the two given distributions. The proposed method is able to effectively compare networks even with different scales, and outperforms the state of the art methods considerably, with respect to the accuracy of the distance function. The datasets and more detailed evaluations are available upon request.

### 1Towards a Faster Network-Centric Subgraph Census

"... Abstract—Determining the frequency of small subgraphs is an important computational task lying at the core of several graph mining methodologies, such as network motifs discovery or graphlet based measurements. In this paper we try to improve a class of algorithms available for this purpose, namely ..."

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Abstract—Determining the frequency of small subgraphs is an important computational task lying at the core of several graph mining methodologies, such as network motifs discovery or graphlet based measurements. In this paper we try to improve a class of algorithms available for this purpose, namely network-centric algorithms, which are based upon the enumeration of all sets of k connected nodes. Past approaches would essentially delay isomorphism tests until they had a finalized set of k nodes. In this paper we show how isomorphism testing can be done during the actual enumeration. We use a customized g-trie, a tree data structure, in order to encapsulate the topological information of the embedded subgraphs, identifying already known node permutations of the same subgraph type. With this we avoid redundancy and the need of an isomorphism test for each subgraph occurrence. We tested our algorithm, which we called FaSE, on a set of different real complex networks, both directed and undirected, showcasing that we indeed achieve significant speedups of at least one order of magnitude against past algorithms, paving the way for a faster network-centric approach.

### Algorithms, Experimentation, Performance

"... In this paper we present an universal methodology for find-ing all the occurrences of a given set of subgraphs in one single larger graph. Past approaches would either enumer-ate all possible subgraphs of a certain size or query a single subgraph. We use g-tries, a data structure specialized in deal ..."

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In this paper we present an universal methodology for find-ing all the occurrences of a given set of subgraphs in one single larger graph. Past approaches would either enumer-ate all possible subgraphs of a certain size or query a single subgraph. We use g-tries, a data structure specialized in dealing with subgraph sets. G-Tries store the topological information on a tree that exposes common substructure. Using a specialized canonical form and symmetry breaking conditions, a single non-redundant search of the entire set of subgraphs is possible. We give results of applying g-tries querying to different social networks, showing that we can efficiently find the occurrences of a set containing subgraphs of multiple sizes, outperforming previous methods.