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‘Co-creation’ in the creative industries
Published in James Juniper, The Economic Philosophy of the Internet of Things, 2018
His 2009 text proposed bigraphs as one modest response to this set of foundational questions. Like an ordinary graph, a bigraph has nodes and edges, and the edges link the nodes, but unlike an ordinary graph, the nodes can be nested inside one another so that a bigraph has both a link structure and a place structure. Bigraphs can encompass specialized versions of both the Pi calculus and Petri nets. Other candidates include Abramsky’s domain theory, Winksel’s event structures, and Hyland’s notion of the effective topos. However, in this chapter, my concerns will be more narrowly focused on the philosophical motivation behind the computational ontologies currently under development and the implications they might have for practices in the social sciences.
Network Clustering
Published in Charu C. Aggarwal, Chandan K. Reddy, Data Clustering, 2018
Srinivasan Parthasarathy, S. M. Faisal
Bipartite graphs are widely used in many graph applications. A bipartite graph (or bigraph) is a special type of graph whose vertices can be divided into two disjoint sets such that no edge connects two vertices from the same set. That is, for graph G=(V,E) the set of vertices V is divided into two sets V1 and V2 such that V1∩V2=Ø and each edge e∈E connects vertices (v1, v2) where v1∈V1 and v2∈V2. Many practical graphs can be represented as a bipartite graph. For example, in a text corpus terms and documents can be represented as a bipartite graph where one set of vertices represents the documents while the other represents terms that appear in the corpus. The edges in the graph represents the co-occurrence of the term and the document in the corpus. Other examples include graphs representing the relationship of buyers and items in a departmental store or reviewers and movies in a movie recommendation system. Bipartite graphs, having been used in the literature to solve clustering problems, are extremely important in Matching Systems partitioning.
A general framework for NCS modeling
Published in Longo Stefano, Tingli Su, Herrmann Guido, Barber Phil, Optimal and Robust Scheduling for Networked Control Systems, 2018
Longo Stefano, Tingli Su, Herrmann Guido, Barber Phil
Here are some basic definitions from graph theory [31]. A graph is defined as a pair G = (V, E) that consists of a set of vertices V and a set of edges E ⊆ V × V where the vertices are υm ∈ V and the edges are em,n = (υm, υn) ∈ E. A graph is called undirected if en,m ∈ E ⇒ em,n ∈ E and directed otherwise. A path is a subgraph π = (V, Eπ) ⊂ G with distinct vertices V = {υ1, υ2, …,υq} and Eπ=def{(υ1,υ2),(υ2,υ3),…,(υq−1,υq)}. A cycle C = (V, EC) is a path (of length q) with an extra edge (υq, υ1) ∈ E. A graph with no cycles is called acyclic. An undirected graph G is called connected if there exists a path π between any two distinct nodes of G (otherwise it is called disconnected). A tree is a connected acyclic graph. A bigraph is a graph whose vertices can be divided into two disjoint sets U1 and U2 such that every edge connects a vertex in U1 to one in U2, i.e. U1 and U2 are independent sets. A bigraph is complete if every vertex of U1 is connected to every vertex of U2. The complete bigraph with partitions of size |U1| = a and |U2| = b, is denoted as Ka,b. A star S is the complete bigraph K1,d, which is a tree with one internal vertex and d surrounding vertices called leaves.
Key web search algorithm based on service ontology
Published in International Journal of Computers and Applications, 2021
In this task, we use the graph of one-factor graph for representation, which is the undirected bigraph suitable to process the optimization task. The factor graph is bigraph, composed of two different types of nodes, variable node and function node respectively, as is shown in Figure 2.
Postulate satisfaction for inconsistency measures in monotonic logics and databases
Published in Journal of Applied Non-Classical Logics, 2023
A bigraph is called an MIS bigraph iff no vertex in V is isolated and for any , .