katz.cent <- function(A, alpha=NULL, beta=NULL){ #NULL sets the default value
    g <- A
    if (class(A) == 'igraph'){
        #Error checking. Turn into adj matrix.
        A <- get.adjacency(A)
    }
    
    lam.dom <- eigen(A)$values[1] #dom eigenvec
    if (is.null(alpha)){
        alpha <- 0.9 * (1/lam.dom) #Set alpha to 90% of max allowed
    }
    
    n <- nrow(A)
    if (is.null(beta)){
        beta <- matrix(rep(1/n, n),ncol=1)
    }
    
    #Katz scores
    scores <- solve(diag(n) - alpha*A,beta)
    names(scores) <- V(g)$name
    
    return(scores)
}

sg.katz <- function(A, alpha=NULL, beta=NULL){
    g <- A
    if (class(A) == 'igraph'){
        # Error checking. Turn into adj matrix if needed.
        A <- get.adjacency(A)
    }
    
    lam.dom <- eigen(A)$values[1] #dom eigenvec
    if (is.null(alpha)){
        alpha <- 0.9 * (1/lam.dom) #Set alpha to 90% of max allowed
    }
    
    A.eigs <- eigen(A) 
    V <- A.eigs$vectors # where columns are the v_i terms
    lams <- A.eigs$values
    n <- length(lams)
    
    # Create subfunction to compute centrality for one node, then use sapply
    # for all nodes
    
    subg.node.i <- function(i){sum(V[i,]^2/(1-alpha*lams))}
    
    subg.all <- sapply(1:n, subg.node.i)
    
    # Add names to output
    names(subg.all) <- V(g)$name
    
    
    return(subg.all)
}