Algorithms For Discovering Communities In Complex Networks

It has been observed that real-world random networks like the WWW, Internet, social networks, citation networks, etc., organize themselves into closely-knit groups that are locally dense and globally sparse. These closely-knit groups are termed communities. Nodes within a community are similar in some aspect. For example in a WWW network, communities might consist of web pages that share similar contents. Mining these communities facilitates better understanding of their evolution and topology, and is of great theoretical and commercial significance. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network, whereas community identification is the problem of identifying the community, to which, a given set of nodes belong. We make a comparative study of various existing community-discovery algorithms. We then propose a new algorithm based on bibliographic metrics, which addresses the drawbacks in existing approaches. Bibliographic metrics are used to study similarities between publications in a citation network. Our algorithm classifies nodes in the network based on the similarity of their neighborhoods. One of the drawbacks of the current community-discovery algorithms is their computational complexity. These algorithms do not scale up to the enormous size of the real-world networks. We propose a hash-table-based technique that helps us compute the bibliometric similarity between nodes in O(m ?) time. Here m is the number of edges in the graph and ?, the largest degree. Next, we investigate different centrality metrics. Centrality metrics are used to portray the importance of a node in the network. We propose an algorithm that utilizes centrality metrics of the nodes to compute the importance of the edges in the network. Removal of the edges in ascending order of their importance breaks the network into components, each of which represent a community. We compare the performance of the algorithm on synthetic networks with a known community structure using several centrality metrics. Performance was measured as the percentage of nodes that were correctly classified. As an illustration, we model the ucf.edu domain as a web graph and analyze the changes in its properties like densification power law, edge density, degree distribution, diameter, etc., over a five-year period. Our results show super-linear growth in the number of edges with time. We observe (and explain) that despite the increase in average degree of the nodes, the edge density decreases with time

251 1 Detecting Communities using Bibliographic Metrics

Abstract — We propose an efficient and novel approach for discovering communities in real-world random networks. Communities are formed by subsets of nodes in a graph, which are closely related. Extraction of these communities facilitates better understanding of such networks. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network where as community identification is the problem of identifying the community to which a given set of nodes from the network belong. In this paper we first give a brief survey of the existing community-discovery algorithms and then propose a novel algorithm to discovering communities using bibliographic metrics. We also test the proposed algorithm on real-world networks and on computer-generated models with known community structures. Index Terms—Community discovery/identification, graph clustering

Bibliometric Approach To Community Discovery

Recent research suggests that most of the real-world random networks organize themselves into communities. Communities are formed by subsets of nodes in a graph, which are closely related. Extracting these communities would lead to a better understanding of such networks. In this paper we propose a novel approach to discover communities using bibliographic metrics, and test the proposed algorithm on real-world networks as well as with computer-generated models with known community structure. Copyright 2005 ACM

Detecting Communities Using Bibliographic Metrics

We propose an efficient and novel approach for discovering communities in real-world random networks. Communities are formed by subsets of nodes in a graph, which are closely related. Extraction of these communities facilitates better understanding of such networks. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network where as community identification is the problem of identifying the community to which a given set of nodes from the network belong. In this paper we first give a brief survey of the existing community-discovery algorithms and then propose a novel algorithm to discovering communities using bibliographic metrics. We also test the proposed algorithm on real-world networks and on computer-generated models with known community structures. © 2006 IEEE

Discovering Communities In Complex Networks

We propose an efficient and novel approach for discovering communities in real-world random networks. Communities are formed by subsets of nodes in a graph, which are closely related. Extraction of these communities facilitates better understanding of such networks. Community related research has focused on two main problems, community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network whereas community identification is the problem of identifying the community to which a given set of nodes from the network belong. In this paper we first perform a brief survey of the existing community-discovery algorithms and then propose a novel approach to discovering communities using bibliographic metrics. We also test the proposed algorithm on real-world networks and on computer-generated models with known community structures. Copyright 2006 ACM

IMPLEMENTATION AND ANALYSIS OF A PARALLEL ALGORITHM FOR RADIOCOLORING

A radiocoloring of a graph G is an assignment to each node, one of the colors 0, 1, 2,... λ such that all pairs of adjacent nodes, get colors which differ by at least two and no pair of nodes at distance two, get the same color. The radiocoloring problem (RCP) consists of determining the minimum λ for a given graph. In this paper, we first implement the PARC (Parallel Algorithm for Radiocoloring) algorithm for radiocoloring which is based on the largest-degree-first coloring heuristic and then perform an analysis of the obtained results. Keywords: Radiocoloring, L(2, 1) labelling, LF algorithm.

PARALLEL ALGORITHM FOR RADIOCOLORING A Graph

Given an undirected graph G(V, E) with vertex set V and edge set E, the Radiocoloring of G is defined as a function f: V → N such that for all pairs of vertices x, y in G |f(x) − f(y) | ≥ 2 when d(x, y) = 1 and |f(x) − f(y) | ≥ 1 when d(x, y) = 2, where d(x, y) is the distance between the vertices x and y and N is the set of nonnegative integers. The range of numbers used is called a span. The radiocoloring problem consists of determining the minimum span for a given graph G. This minimum span of G is called the radiochromatic number, λ of G. In this paper, we discuss Nordhaus-Gaddum type result for the sum and product of the radiochromatic number of a graph and that of its complement. We also propose an approximate parallel algorithm for radiocoloring. Our algorithm is based on the largest-degree-first coloring heuristic

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