Implicit graphIn the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented as explicit objects in a computer's memory, but rather are determined algorithmically from some other input, for example a computable function. The notion of an implicit graph is common in various search algorithms which are described in terms of graphs. In this context, an implicit graph may be defined as a set of rules to define all neighbors for any specified vertex.
Brain tumorA brain tumor occurs when abnormal cells form within the brain. There are two main types of tumors: malignant tumors and benign (non-cancerous) tumors. These can be further classified as primary tumors, which start within the brain, and secondary tumors, which most commonly have spread from tumors located outside the brain, known as brain metastasis tumors. All types of brain tumors may produce symptoms that vary depending on the size of the tumor and the part of the brain that is involved.
Cerebral arteriovenous malformationA cerebral arteriovenous malformation (cerebral AVM, CAVM, cAVM, brain AVM, or BAVM) is an abnormal connection between the arteries and veins in the brain—specifically, an arteriovenous malformation in the cerebrum. The most frequently observed problems related to a cerebral arteriovenous malformation (AVM) are headaches and seizures, cranial nerve afflictions including pinched nerve and palsy, backaches, neckaches, and nausea from coagulated blood that has made its way down to be dissolved in the cerebrospinal fluid.
Star (graph theory)In graph theory, a star S_k is the complete bipartite graph K_1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define S_k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves. A star with 3 edges is called a claw. The star S_k is edge-graceful when k is even and not when k is odd. It is an edge-transitive matchstick graph, and has diameter 2 (when l > 1), girth ∞ (it has no cycles), chromatic index k, and chromatic number 2 (when k > 0).
HydrocephalusHydrocephalus is a condition in which an accumulation of cerebrospinal fluid (CSF) occurs within the brain. This typically causes increased pressure inside the skull. Older people may have headaches, double vision, poor balance, urinary incontinence, personality changes, or mental impairment. In babies, it may be seen as a rapid increase in head size. Other symptoms may include vomiting, sleepiness, seizures, and downward pointing of the eyes. Hydrocephalus can occur due to birth defects or be acquired later in life.
GraphonIn graph theory and statistics, a graphon (also known as a graph limit) is a symmetric measurable function , that is important in the study of dense graphs. Graphons arise both as a natural notion for the limit of a sequence of dense graphs, and as the fundamental defining objects of exchangeable random graph models. Graphons are tied to dense graphs by the following pair of observations: the random graph models defined by graphons give rise to dense graphs almost surely, and, by the regularity lemma, graphons capture the structure of arbitrary large dense graphs.
AssortativityAssortativity, or assortative mixing, is a preference for a network's nodes to attach to others that are similar in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's degree. The addition of this characteristic to network models more closely approximates the behaviors of many real world networks. Correlations between nodes of similar degree are often found in the mixing patterns of many observable networks.
