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***Agnatic (Uterine) Weight – It is the number of individuals whose linear agnatic (uterine) ascendant of a given generation is known, as a percentage of all individuals for whom the at least one (agnatic or uterine) ascendant of that generation is known.
***Agnatic (Uterine) Net Weight - It is the number of individuals for whom only the agnatic (uterine) ascendant of a given generation is known, as a percentage of individuals for whom at least one (agnatic or uterine) ascendant of that generation is known.
***Alliance Matrix – It is the matrix of a matrimonial alliance network. It is a contingency (or cross) weighted table that indicates the number of spouses "exchanged" between a given set of classes/groups of individuals. As the classes are listed in the first top-line and first left-column, the descending diagonal of the matrix represent the endogamic (intra-group) marriages.
***Bicomponent - A bicomponent (or bi-connected component) is a graph where two distinct Paths can connect any two vertices to each other. Thus, a bicomponent contains no cut-point whose elimination would cut it into two disconnected components. Consequently, any two vertices in a bicomponent form part of a cycle (Grange & Houseman, 2010; Hamberger & Daillant, 2008).
Cycle - A cycle is a path where the first and the last vertex are identical. Using this notion presuppose an ego-centered view of kinship ties.
Circuit - A circuit is a (sub)graph whose vertices and arcs form a single cycle. Using this notion presuppose a socio-centered view of kinship ties.
Circuit Census - See matrimonial census.
***Circuit Composition Table – It is a symmetrical cross table that indicates which matrimonial circuit type is the product of the intersection of two other types of circuit (for an example of a circuit composition table, limited to the third canonical degree, see Hamberger & Daillant, 2009).
***Circuit Intersection Matrix – It is the matrix of a circuit intersection network. It indicates the occurrences of each circuit type, as well as the number of marriages involved in a circuit intersection.
***Circuit Intersection Network – It is the network of all the circuit intersections in a given kinship network. It shows both the occurrences of each circuit type, and the number of marriages involved in each circuit intersection.
***Classificatory Matrimonial Census – It is a specific kind of matrimonial census. It consists in searching not for individual circuit types, but for classes of circuit types, that share a given formal criterion.
***Concordance Table - A concordance table is a file containing information about the renumbering of individuals. It is a simple text file with two columns where the Id numbers of the members of the second and the first corpus are listed. Individuals that appear in only one corpus do not have to be listed in this table, and numbers need not to be ordered.
***Connubial Circuit – It is a circuit as part of a matrimonial alliance network.
***Core - The core of a kinship network is the sum of its matrimonial bicomponents.
***Frame - The frame of a matrimonial circuit is the graph obtained by replacing each one of its consanguine chains with a simple arc. Consequently, only two types of lines compose it: the marriages and the consanguine ties. The frame of a matrimonial network is the union of all the circuit frames that compose the network.
***Generation - Generation and generational distance are not unique concepts. Except in kinship networks that consist of trees, there are usually several alternative ways to arrange an individual on a generational level inferior to its ascendants and superior to its descendants. For instance, if a man has married his sister's daughter, his children will be at the same time grandchildren and great-grandchildren of his father. One has to decide on the path along which generational distance shall be calculated.
The algorithm used by Puck is identical to that of Pajek. It consists in navigating through the network along kinship paths and assigning to parents, spouses and children of each individual the generational level of that individual, augmented by 1, 0 or -1 according to the nature of the kinship tie.
Note: The identity of the algorithm does not necessarily imply the network of the results. The result depends on the navigation path, which may be different for Pajek and Puck, since arcs are not necessarily stored in the same order.
***Kernel - The kernel of a kinship network is its largest matrimonial bicomponent.
***Kinship Network - "Kinship networks are characterized by the interplay of three fundamental principles: filiation, marriage, and gender. We ordinarily represent filiation by a set of arcs (descent arcs) that are directed from parents to children, and marriage by a set of undirected edges (marriage edges) between spouses (for alternative representations of kinship networks without edges, see below). Kinship networks thus are mixed graphs, containing both arcs and edges. Gender is usually taken into account by a partitioning of the vertex set (the gender partition), usually into two or three disjoint classes (male, female, and possibly unknown sex)" (Hamberger, Houseman, & White, 2012).
***Matrimonial Alliance Network – It is a network of marriage ties between groups (classes) of individuals. In a matrimonial alliance network, arcs represent (one or more) marriage ties and point from the wife's to the husband's group ; nodes represent groups of individuals, who share a given property (place of residence, consanguinity...).
Matrimonial Bicomponent - A matrimonial bicomponent is a maximal subgraph in which every two vertices are part of a matrimonial circuit. Also, any two vertices in a matrimonial bicomponent can be linked to each other by two distinct kinship chains that do not pass through and do not meet in “structural children”. Matrimonial bicomponents are closely related (but not identical) to matrimonial components : both are line-biconnected (two distinct line-series link each vertex to every other), but matrimonial bicomponents are also vertex-biconnected (the two interconnecting line-series never run through the same vertex).
Matrimonial Circuit - A matrimonial circuit is a kinship chain that both is closed by a marriage and do not involve childless and unmarried individuals (Hamberger, Houseman, Daillant, White, & Barry, 2004).
Pragmatically, matrimonial circuit types correspond to types of consanguine marriage (between consanguine kin, such as between a man and his mother’s brother’s daughter) and types of affine “relinkings” incorporating one, two or more intermediary marriage ties.
- Consanguine marriages, that incorporate a single marriage tie (and a single consanguine kinship chain), form matrimonial circuits of “width” 1, e.g. a man marries his mother’s brother’s daughter.
- Relinkings incorporating two marriage ties (and two consanguine kinship chains), form matrimonial circuits of “width” 2, e.g. a man and his sister marry a sister and her brother, or a man marries his mother’s brother’s wife’s bother’s daughter.
- Relinkings incorporating three marriage ties (and three consanguine kinship chains) form matrimonial circuits of “width” 3, e.g. a man marries his mother’s brother’s wife’s bother’s daughter’s husband’s sister.
Matrimonial circuits are indicators of sociological constraints of matrimonial choice (rules, preferences and avoidances, opportunities) and of the dynamics of self-organization of the network. They have to be studied as a whole. For the concept of the matrimonial circuit, see Hamberger, Houseman, & White (2012, p. 539‑540).
***Matrimonial Constellation – It is the largest component of a matrimonial network frame.
***CORR? Matrimonial Network - A matrimonial network is a subgraph induced by matrimonial circuits. Matrimonial networks are line-induced and not vertex-induced subgraphs. This means that every line of the subgraph is part of a circuit (it is not enough that its endpoints are in a circuit). The matrimonial network derived from a set of matrimonial circuits found in a kinship network is thus simply the network composed of these circuits. It consists, in other word, of the matrimonially “interesting” regions of the original kinship network.
The connected parts of the matrimonial network (the matrimonial components) represent continuous regions of densely interconnected circuits, which may be studied from various perspectives.
On the one hand, we may suppose that the frequent occurrence of particular matrimonial patterns is correlated with other properties of the network region concerned (for instance social class, geographical region or historical period); we may then apply several partitions to the network in order to evaluate the degree to which partition clusters correspond to matrimonial components.
On the other hand, we may interpret the density of circuits as an effect of self-reinforcing social mechanisms (behavior transmission, imitation or the presence of rules) or as a simple network effect (rings combining to compose other circuits) which we did not consider when defining the criteria for our initial circuit search.
The concept of a matrimonial network is also meaningful in and of itself, independent of any particular circuit set. Even without being able to precisely identify all matrimonial circuits (without limits of size) which may exist in a kinship network, it is possible to determine which part of the network is composed of matrimonial circuits. The result is the absolute matrimonial network, the subgraph induced by all lines in the network which are in some circuit whatsoever. This absolute matrimonial network is equivalent to the sum of all matrimonial bicomponents. It corresponds to what has been called the “core” in a P-graph context (Grange & Houseman, 2010; White & Houseman, 1996) .
Every matrimonial network constitutes a network without tails (every vertex must have a degree greater than one) and without structural children (every vertex must have an outdegree greater than zero). However, the reverse is not the case. There may be networks where all vertices fulfil these two-degree criteria, but which nevertheless are not matrimonial, as they contain lines which do not form part of any matrimonial circuit. Filial triads (father, mother and child) or marriage ties connecting disjoint matrimonial components are instances of this.
***Mean Genealogical Depth – It is the mean genealogical distance from apical ascendants, it is calculated with the Cazes formula (Cazes, & Cazes, 1996).
Ore-graphs - Named after the scandinavian mathematician Oystein Ore (1970), developed by Vladimir Batagelj and Andrej Mrvar. In an Ore graph, vertices represent individuals, arcs filial ties and edges marriages. Vertex-labels represent gender; two different types of lines represent paternal and maternal ties.
P-graph - Developed by Douglas White and Paul Jorion (White, & Jorion, 1992), used by the homonymous computer program p-graph. In a P-graph couples or unmarried individuals are represented by vertices, married individuals by gender labeled lines running from the couple in which they are partner to the couple of which they are born.
P-graphs have the advantages of being directed acyclic and of incorporating fewer lines and vertices, allowing semi-cycles (that correspond to matrimonial circuits in Ore-graphs) to be more easily detected. Note, however, that an individual who marries several times will be represented by several lines. Lines therefore have to be name-labeled in order to distinguish identity from siblingship.
***Relation Census – It is a census of kinship relations that: whether comply with some given quantitative (size) or qualitative (formula) criteria; or correspond to the criteria established in a matrimonial census.
***Structural Children - In a kinship network, structural children are individuals who do not have neither spouses nor children.
Tip-graph - Named after the research group TIP (Traitement Informatique de la Parenté), used by the macros of the Tip4Pajek series (2007). In a Tip-graph, filial and marriage ties are represented by arcs. All information on the type of tie and on gender is contained in line values. There are five types of lines:
- a marriage arc pointing from female to male,
- a filial arc pointing from female (mother) to female (daughter),
- a filial arc pointing from female to male (son),
- a filial arc pointing from male (father) to female,
- a filial arc pointing from male to male.
Because a Tip-Graph does not involve vertex labeling, it is a highly economical representation of a kinship network. Its major disadvantage is that it is not directed acyclic. Many analyses therefore require its being re-transformed into a conventional Ore-graph. To export a dataset in tip-graph format (as a pajek project file) the option “tip” has to be chosen.
***Virtual Individuals - Virtual individuals are individuals for whom no information is available except for their kinship relations (and perhaps their gender, if they are parents or spouses of existing individuals). They only serve to represent the common parents of full siblings.