|
Clique Percolation Method
The clique percolation method is a popular approach for analyzing the overlapping community structure of networks. The term ''network community'' (also called a module, cluster or cohesive group) has no widely accepted unique definition and it is usually defined as a group of nodes that are more densely connected to each other than to other nodes in the network. There are numerous alternative methods for detecting communities in networks, for example, the Girvan–Newman algorithm, hierarchical clustering and modularity maximization. Definitions Clique Percolation Method (CPM) The clique percolation method builds up the communities from ''k''-cliques, which correspond to complete (fully connected) sub-graphs of ''k'' nodes. (E.g., a ''k''-clique at ''k'' = 3 is equivalent to a triangle). Two ''k''-cliques are considered adjacent if they share ''k'' − 1 nodes. A community is defined as the maximal union of ''k''-cliques that can be reached from each other t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Community Structure
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping) sets of nodes such that each set of nodes is densely connected internally. In the particular case of ''non-overlapping'' community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But ''overlapping'' communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to. Properties In the study of networks, such as computer and information networks, social networks and biological networks, a number of different charac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, an undirected hypergraph H is a pair H = (X,E) where X is a set of elements called ''nodes'' or ''vertices'', and E is a set of non-empty subsets of X called ''hyperedges'' or ''edges''. Therefore, E is a subset of \mathcal(X) \setminus\, where \mathcal(X) is the power set of X. The size of the vertex set is called the ''order of the hypergraph'', and the size of edges set is the ''size of the hypergraph''. A directed hypergraph differs in that its hyperedges are not sets, but ordered pairs of subsets of X, with each pair's first and second entries constituting the tail and head of the hyperedge respectively. While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same card ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Networks
Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics * Networks, a graph with attributes studied in network theory ** Scale-free network, a network whose degree distribution follows a power law ** Small-world network, a mathematical graph in which most nodes are not neighbors, but have neighbors in common * Flow network, a directed graph where each edge has a capacity and each edge receives a flow Biology * Biological network, any network that applies to biological systems * Ecological network, a representation of interacting species in an ecosystem * Neural network, a network or circuit of neurons Technology and communication * Artificial neural network, a computing system inspired by animal brains * Broadcast network, radio stations, television stations, or other electronic media outlets ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Community Structure
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping) sets of nodes such that each set of nodes is densely connected internally. In the particular case of ''non-overlapping'' community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But ''overlapping'' communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to. Properties In the study of networks, such as computer and information networks, social networks and biological networks, a number of different charac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics. Social networks and the analysis of them is an inherently interdisciplinary academic field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing the dynamics of triads and "web of group affiliations". Jacob Moreno is credited with developing the first sociograms in the 1930s to study interpersonal relationships. These approaches were mathematically formalize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metastasis
Metastasis is a pathogenic agent's spread from an initial or primary site to a different or secondary site within the host's body; the term is typically used when referring to metastasis by a cancerous tumor. The newly pathological sites, then, are metastases (mets). It is generally distinguished from cancer invasion, which is the direct extension and penetration by cancer cells into neighboring tissues. Cancer occurs after cells are genetically altered to proliferate rapidly and indefinitely. This uncontrolled proliferation by mitosis produces a primary heterogeneic tumour. The cells which constitute the tumor eventually undergo metaplasia, followed by dysplasia then anaplasia, resulting in a malignant phenotype. This malignancy allows for invasion into the circulation, followed by invasion to a second site for tumorigenesis. Some cancer cells known as circulating tumor cells acquire the ability to penetrate the walls of lymphatic or blood vessels, after which they are abl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the Mathematics, mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, and neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics develop the Phenomenology (particle physics), phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of classical mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation
Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation. Background During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology, and other fields. For example, in geology, percolation refers to filtration of water through soil and permeable rocks. The water flows to recharge the groundwater in the water table and aquifers. In places where infiltration basins or septic drain fields are planned to dispose of substantial amounts of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Rényi Model
In the mathematical field of graph theory, the Erdős–Rényi model is either of two closely related models for generating random graphs or the evolution of a random network. They are named after Hungarian mathematicians Paul Erdős and Alfréd Rényi, who first introduced one of the models in 1959, while Edgar Gilbert introduced the other model contemporaneously and independently of Erdős and Rényi. In the model of Erdős and Rényi, all graphs on a fixed vertex set with a fixed number of edges are equally likely; in the model introduced by Gilbert, also called the Erdős–Rényi–Gilbert model, each edge has a fixed probability of being present or absent, independently of the other edges. These models can be used in the probabilistic method to prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs. Definition There are two closely related variants of the Erdős–R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Motif
Network motifs are recurrent and statistically significant Subgraph (graph theory), subgraphs or patterns of a larger complex network, graph. All networks, including biological networks, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as graphs, which include a wide variety of subgraphs. Network motifs are sub-graphs that repeat themselves in a specific network or even among various networks. Each of these sub-graphs, defined by a particular pattern of interactions between vertices, may reflect a framework in which particular functions are achieved efficiently. Indeed, motifs are of notable importance largely because they may reflect functional properties. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks. Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challengi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
